Physics, 16.10.2019 05:30 Sinless60951

A) one strategy in a snowball fight the snowball at a hangover level ground. while your opponent is watching this first snowfall, you throw a second snowball at a low angle and time it to arrive at the same time as the first. assume both snowballs are the one with the same initial speed 14.1 m/s. the first snow ball is thrown at an angle of 52° above the horizontal. at what angle sure you throw the second snowball to make ahead the same point as the first? acceleration of gravity is 9.8 m/s^2. answer in units of °.
b) how many seconds after the first snowball should be through the second so that they arrive on target at the same time? answer in units of s.

Answers: 2

Show answers

Answers

Answer from: bettybales1986

Answers:

a) $\theta_{2}=38\°$

b) t=0.495 s

Explanation:

This situation is a good example of the projectile motion or parabolic motion, in which the travel of the snowball has two components: x-component and y-component. Being their main equations as follows for both snowballs:

Snowball 1:

x-component:

$x=V_{o}cos\theta_{1} t_{1}$ (1)

Where:

$V_{o}=14.1 m/s$ is the initial speed of snowball 1 (and snowball 2, as well)

$\theta_{1}=52\°$ is the angle for snowball 1

$t_{1}$ is the time since the snowball 1 is thrown until it hits the opponent

y-component:

$y=y_{o}+V_{o}sin\theta_{1} t_{1}+\frac{gt_{1}^{2}}{2}$ (2)

Where:

$y_{o}=0$ is the initial height of the snowball 1 (assuming that both people are only on the x axis of the frame of reference, therefore the value of the position in the y-component is zero.)

y=0 is the final height of the snowball 1

$g=-9.8m/s^{2}$ is the acceleration due gravity (always directed downwards)

Snowball 2:

x-component:

$x=V_{o}cos\theta_{2} t_{2}$ (3)

Where:

$\theta_{2}$ is the angle for snowball 2

$t_{2}$ is the time since the snowball 2 is thrown until it hits the opponent

y-component:

$y=y_{o}+V_{o}sin\theta_{2} t_{2}+\frac{gt_{2}^{2}}{2}$ (4)

Having this clear, let's begin with the answers:

a) Angle for snowball 2

Firstly, we have to isolate $t_{1}$ from (2):

$0=0+V_{o}sin\theta_{1} t_{1}+\frac{gt_{1}^{2}}{2}$ (5)

$t_{1}=-\frac{2V_{o}sin\theta_{1}}{g}$ (6)

Substituting (6) in (1):

$x=V_{o}cos\theta_{1}(-\frac{2V_{o}sin\theta_{1}}{g})$ (7)

Rewritting (7) and knowing $sin(2\theta)=sen\theta cos\theta$ :

$x=-\frac{V_{o}^{2}}{g} sin(2\theta_{1})$ (8)

$x=-\frac{(14.1 m/s)^{2}}{-9.8 m/s^{2}} sin(2(52\°))$ (9)

x=19.684 m (10) This is the point at which snowball 1 hits and snowball 2 should hit, too.

With this in mind, we have to isolate $t_{2}$ from (4) and substitute it on (3):

$t_{2}=-\frac{2V_{o}sin\theta_{2}}{g}$ (11)

$x=V_{o}cos\theta_{2} (-\frac{2V_{o}sin\theta_{2}}{g})$ (12)

Rewritting (12):

$x=-\frac{V_{o}^{2}}{g} sin(2\theta_{2})$ (13)

Finding $\theta_{2}$ :

$2\theta_{2}=sin^{-1}(\frac{-xg}{V_{o}^{2}})$ (14)

$2\theta_{2}=75.99\°$

$\theta_{2}=37.99\° \approx 38\°$ (15) This is the second angle at which snowball 2 must be thrown. Note this angle is lower than the first angle $(\theta_{2} < \theta_{1})$ .

b) Time difference between both snowballs

Now we will find the value of $t_{1}$ and $t_{2}$ from (6) and (11), respectively:

$t_{1}=-\frac{2V_{o}sin\theta_{1}}{g}$

$t_{1}=-\frac{2(14.1 m/s)sin(52\°)}{-9.8m/s^{2}}$ (16)

$t_{1}=2.267 s$ (17)

$t_{2}=-\frac{2V_{o}sin\theta_{2}}{g}$

$t_{2}=-\frac{2(14.1 m/s)sin(38\°)}{-9.8m/s^{2}}$ (18)

$t_{2}=1.771 s$ (19)

Since snowball 1 was thrown before snowball 2, we have:

$t_{1}-t=t_{2}$ (20)

Finding the time difference between both:

$t=t_{1}-t_{2}$ (21)

t=2.267 s - 1.771 s

Finally:

t=0.495 s

Answer from: Quest

Gravity bc it’s gravity

Answer from: Quest

i had this question and the answer was 3.15 miles.

martina travels from school to her mom's office. from there, she walks to school. after school, she walks to the library and then to a friends house before finally ending back at home. find martina's total distance traveled.

a) 0 miles

b) 0.4 miles

c) 1 mile

d) 3.15 miles

Other questions on the subject: Physics

Physics, 22.06.2019 15:40, winterblanco

Question 1 what is amperage? is the rate of doing work. is the rate of flow of protons in electric current. represents the amount of pressure behind electron flow. is the rate of flow of electrons in electric current. 2 points question 2 what is voltage? is the rate of doing power. represents the amount of pressure behind electron flow. is the rate of doing work. is the rate of flow of electrons in electric current. 2 points question 3 what is power? is the rate of flow of protons in electric current. is the rate of flow of electrons in electric current. is the rate of doing work. represents the amount of pressure behind electron flow. 2 points question 4 if we multiply volts times amps we get what? power circuit work current 2 points question 5 what are two ways alternating currents are similiar? in both ac and dc electrons flow in the same pattern. in both ac and dc, the flow of electrons changes directions back and forth. both ac and dc are only possible in certain materials with atoms that will allow electron flow. both ac and dc involve the flow of electrons. 4 points question 6 how does the flow of electrons flow in an alternating current? the flow of electrons is always slower in an alternating current than within a direct current. the flow of electrons is not constant and forward; it changes direction back and forth. electrons flow from from a higher affinity to that of a lower affinity. electron flow is constant and only in a forward direction. 2 points question 7 what is the flow like in a direct current? the flow of electrons is not constant and forward; it changes direction back and forth. the flow of electrons is constant and only in a forward direction. the flow of electrons go from a higher affinity to a lower affinity. the flow of electrons are always faster in a direct current. 2 points question 8 how is an electric current able to flow? electrons flow from the higher affinity to lower affinity and electrical current is generated. protons flow from the higher affinity to lower affinity and electrical current is generated. the movement of protons from one atom to another leads to an electric charge. the movement of electrons from one atom to another atom in a line results in a flow of electric current. 2 points question 9 how do electrons move from the two different types of metal in a battery? protons flow from the metal with the lower affinity to the metal with higher affinity and electrical current is generated. electrons flow from the metal with the lower affinity to the metal with higher affinity and electrical current is generated. electrons flow from the metal with the higher affinity to the metal with lower affinity and electrical current is generated. protons flow from the metal with the higher affinity to the metal with lower affinity and electrical current is generated.

Answers: 2

continue

Physics, 22.06.2019 18:00, championroof

Acid precipitation chemically weathering a 5.0-kg limestone rock . which coukd be the result ?

Answers: 1

continue

Physics, 22.06.2019 22:00, tewilliams1

If anyonee has done the momentum lab practical in physics can you give me the answers i am s lostt rnn : (

Answers: 2

continue

Physics, 23.06.2019 00:20, bighoneypadrick

An object with a mass of 1.5 kg changes its velocity from + 15 m/s to +22 m/s during a time interval of 3.5 seconds. what impulse was delivered to the objects?

Answers: 2

continue

You know the right answer?

A) one strategy in a snowball fight the snowball at a hangover level ground. while your opponent is...