Question

A runaway train speeds horizontally off a 500.0-m-high cliff. Ignore air resistance for all parts. (a) How long does the train spend in the air? (b) How fast did the train leave the cliff top to land on level ground below, 900.0 m from the base of the cliff? Give your answer in miles per hour. (c) What is the velocity (magnitude and direction) of the train 5 seconds after leaving the cliff? Give your answer with respect to the positive x-axis.

Answer 1

The train can be considered as a horizontal projectile. The initial height of the projectile is h = 500m.

(a) The time the train spendd in air is the time of flight of the horizontal projectile, giveen by,

So the train spent 10.10s on air.

(b) Given the range of the projectile R = 900m. If u is the initial velocity of the projectile, then

So the velocity of the train was 199.35 miles/hr.

(c) The x-component of velocity after a time t = 5s is given by,

The y-component of velocity after a time t = 5s is given by,

The magnitude of velocity is given by,

So the magnitude of velocity of the train 5 seconds after leaving the cliff is 227.47 miles/hr.

The direction of velocity is given by,

So the direction of velocity vector of the train 5 seconds after leaving the cliff is downwards from the positive x -axis.