Aball is thrown into the air by a baby alien on a planet in the system of alpha centauri with a velocity of 35 ft/s. its height in feet after t seconds is given by y=35t−26t2. a. find the average velocity for the time period beginning when t=3 and lasting .01 sec : .005 sec : .002 sec : .001 sec : note: for the above answers, you may have to enter 6 or 7 digits if you are using a calculator. b. estimate the instantaneous velocity when t=3.

Part A:

(a): -121.26 ft/s.

(b): -121.13 ft/s.

(c): -121.052 ft/s.

(d): -121.026 ft/s.

Part B:

-121.00 ft/s.

Explanation:

Given that the height of the balloon after t seconds is

The average velocity of an object is defined as the total distance traveled by the object divided by the time taken in covering that distance.

where,

are the positions of the object at time and respectively.

Part A:For the average velocity for the time period beginning when t=3 and lasting .01 sec.

For this case,

For the average velocity for the time period beginning when t=3 and lasting .005 sec.

For this case,

For the average velocity for the time period beginning when t=3 and lasting .002 sec.

For this case,

For the average velocity for the time period beginning when t=3 and lasting .001 sec.

For this case,

Part B:

The instantaneous velocity of the balloon at the given time is defined as the rate of change of its position at that time.

Note: The negative sign with all the velocities indicates that the direction of these velocities are downwards.

Distance^2= yellow line ^2 (see picture) = 30^2 + 49^2so distance = squareroot of (300^2 +49^2)i dont know if this is how to solve it, but i cnt think of another way

Rain is pulled by gravity which is a non contact force