Question

Imagine someone in a train drops their tea cup at a height of 1.25 meters above the floor of the train. the train is moving at a constant velocity of 15 m/s ( in a straight line)

a. how long will it take for it to hit the floor?
b. how far will the train have traveled from when the cup is dropped to when it hits the floor?

Answer 1

The train will have traveled a distance of 7.5 meters from when the cup is dropped to when it hits the floor.

Step-by-step explanation:

To find the distance the train will have traveled from when the tea cup is dropped to when it hits the floor, we need to determine how long it takes for the cup to hit the floor. Since the cup is dropped vertically and the train is moving in a straight line horizontally, we can treat the horizontal and vertical motions as independent.

The time it takes for an object to fall vertically can be found using the equation: d = 0.5 * g * t^2, where d is the distance fallen, g is the acceleration due to gravity (9.8 m/s^2), and t is the time.

Since the cup falls from a height of 1.25 meters, we can solve for t as follows: 1.25 = 0.5 * 9.8 * t^2. Solving for t, we find t = 0.5 seconds.

The horizontal distance the train travels in this time can be found using the equation: d = v * t, where d is the distance traveled, v is the velocity of the train (15 m/s), and t is the time. Substituting in the values, we find d = 15 * 0.5 = 7.5 meters.

Therefore, the train will have traveled a distance of 7.5 meters from when the cup is dropped to when it hits the floor.