Physics, 16.11.2020 16:40 Cooldude497

A model rocket Was built last weekend. We launched it in a nearby field. The rocket took off Straight up with an initial velocity 62.3 m/s. If it accelerates upward at 4.30 m/s2 until the engines stop 3.73 s later: (a) What is the maximum height the rocket reaches? (b) How long is the rocket in the air? (c) What is the velocity of the rocket as it hits the ground?

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Answer from: Danay4600

a) y_total = 575.4 m , b) t_total = 22.56 s , c) v = 106.20 m

Explanation:

a) We can solve this exercise using the scientific relations

Let's find the height reached while the engines are running

v₁ = v₀ + a t

v₁ = 62.3 + 4.30 3.73

v₁ = 78.339 m / s

in this time it rose

y₁ = v₀ t₁ + ½ a t₁²

y₁ = 62.3 3.73 + ½ 4.30 3.73²

y₁ = 262.29 m

At this moment the engines are turned off and the rocket continues in a vertical launch, suppose that the acceleration of gravity is constant in this path

v₂ = v₁ 2 - 2 g y₂

at maximum height the velocity is zero (v₂ = 0)

y₂ = v₁ 2 / 2g

y₂ = 78.339 2/2 9.8

y₂ = 313.11 m

the total height is

y_total = y₁ + y₂

y_total = 262.29 + 313.11

y_total = 575.4 m

b) the time the rocket is in the air is

t_total = t₁ + t₂

where t₂ is the time after the engines have shut down

y = y₁ + v₁ t₂ - ½ g t₂²

y = 0

0 = 262.29 + 78.339 t₂ - ½ 9.8 t₂²

t₂² - 15.99 t₂ - 53.53 = 0

t₂ = [15.99 ±√ (15.99² +4 53.53)] / 2

t₂ = [15.99 ± 21.67] / 2

t₂´ = 18.83 s

t₂´´ = -2.84 s

since the time must be a positive quantity the correct result is t2 = 18.83 s, the total time in the air is

t_total = 3.73 + 18.83

t_total = 22.56 s

c) the speed when it hits the ground

We can perform this calculation starting with the maximum height y = 575.4 m where it has zero initial velocity (vo = 0)

v² = v₀² + 2 g y

v = √ 2gy

v = √ (2 9.8 575.4)

v = 106.20 m

Answer from: Quest

no simpler subs form complex ones. synthesise = make

Answer from: Quest

Then the answer would be d then

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A model rocket Was built last weekend. We launched it in a nearby field. The rocket took off Straigh...