Find the speed of the train?

Question

A passenger in a train that moves horizontally looks outside and sees a child hitting a ball straight up to a height of 30 m.The child's coach clains that the ball left the child and a angle of 15 degree above the horizon. Find the speed of the train relative to the ground.

Answer 1

Vertical speed of ball:

v^2 - u^2 = 2as

v = speed at top = 0
u = initial speed
a = -9.81 m/s^2
s = 30 m

Therefore: u^2 = 2 x 9.81 x 30

u = sqrt(2 x 9.81 x 30)
= 24.26 m/s

Horizontal Speed of Train = x

Drawing a triangle, we see that

tan (15) = 24.26 / x

x = 24.26 / tan (15)
= 90.5 m/s relative to ground

Answer 2

I won't hand you the answer but will tell you how to solve it. The train is moving at the same speed as the horizontal velocity of the ball. From height=.5*g*t^2 you can find the time, and from v=g*t the initial vertical velocity v0. Then the horizontal velocity = v0/tan(15 deg). That's some fast train; Tres Grande Vitesse or something similar, I think.

Answer 3

Go up to the conductor and ask him how fast is the train going. If you can't do that, ask your teacher for additional help.