Question

A model train engine was moving at a constant speed on a straight horizontal track. As the engine moved​ along, a marble was fired into the air by a spring in the​ engine's smokestack. The​ marble, which continued to move with the same forward speed as the​ engine, rejoined the engine 1 sec after it was fired. The measure of the angle the​ marble's path made with the horizontal was 61degrees. Use the information to find how high the marble went and how fast the engine was moving.

Answer 1

Answer:

The marble was moving in a projectile and the speed of the engine was 2.716 m/s

Explanation:

The vertical component of the marble's flight path relative to the train

is given by the equation y(t) = v*t - (4.9)*t^2,

where, v is the initial upward velocity of the marble relative to the train.  

So with y(1) = v - 4.9 = 0 we have  

v = 4.9 m/s.

The marble will reach maximum height after 0.5 seconds, at which the

height will be y(0.5) = (4.9)*(0.5) - (4.9)*(0.5)^2 = (4.9)*(0.25) = 1.225 m.

Now,  the marble has a vertical velocity component of 4.9 m/s and a horizontal velocity component

of V m/s such that tan(61) = 4.9 / V

V = 4.9 / tan(61) = 2.716 m/s

This horizontal velocity component of the marble is the same as the

speed of the train i.e. 2.716 m/s.