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 ?

Answer 1

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 )