projectile motion

2010-07-18 12:16 am

Mary is sitting in a car which is moving up a slope of 30 degree with a constant speed of 70km/h . After travelling for 10s from the foot of slope X, she release a ball. The ball hits the ground at Y.
Find the distance from the starting point to Y.

回答 (1)

六呎將軍

2010-07-18 1:49 am

✔ 最佳答案

Converting to unit of m/s, initial velocity of the ball = 70/3.6 = 19.44 m/s

Also inclination of initial velocity = 30 deg.

Then, in the 10 s interval, distance travelled by the car = 194.4 m

With vertical height above Y = 194.4 sin 30 = 97.2 m

So, considering the vertical part of the projectile motion of the ball, we have:

(19.44 sin 30)T - 5T2 = -97.2 where T is the time of flight

9.72T - 5T2 = -97.2

5T2 - 9.72T - 97.2 = 0

T = 5.49 s

Thus, horizontal distance travelled, also the distance from the starting point to Y, is:

5.49 x 19.44 cos 30 = 92.4 m

參考: Myself

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