Upon landing on an alien planet which lacks an atmosphere, you perform an experi

Question

Upon landing on an alien planet which lacks an atmosphere, you perform an experiment designed to determine the acceleration due to gravity.
A small but powerful cannon fires a ball directly upwards from ground level with the ball leaving the cannon with a speed of 37.5 m/s.
The ball is measured to reach a maximum height of 311.0 m.

(11.1) What is the acceleration due to gravity on this planet ?

(11.2) How much time elapses between the ball leaving the cannon and the ball hitting the ground ?

(11.3) With what speed is the ball traveling just before it hits the ground ?

Explanation / Answer

in vertical,

v0 = 37.5 m/s

yf - yi = 311 m

at maximum height, vf = 0

Applying vf^2 - vi^2 = 2 a y

0^2 - 37.5^2 = 2(-a)(311)

a = 2.26 m/s^2 ..........Ans

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when it comes back to initial position then

y = yf - yi = 0

yf - yi = v0 t +a t^2 / 2

0 = 37.5 t - 2.26 t^2 / 2

t = 33.2 sec

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Applying vf = vo + a t

v = (37.5) - (2.26)(33.2) = - 37.5 m/s

Speed is 37.5 m/s (minus represents that ball is moving downwrads )

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