A passenger riding on a train moving over a bridge with a velocity of 55m/s, drops a pen out of the window. the pen lands in the river below 2.4 seconds later.
A. find how high the window was above the water.
B. how far forward did the pen move?
To answer these two questions, we need to break down the problem into different components and examine the motion of the train and the pen separately.
First, let's consider the motion of the train. We are given that the train's velocity is 55 m/s. However, we are not given any information about its acceleration or deceleration, so we can assume that the train is moving with constant velocity.
A. Finding the height of the window above the water:
Since the train's velocity is constant, its vertical motion does not affect the pen's trajectory. Therefore, we can assume that the only motion affecting the vertical distance is the free fall of the pen.
To find the height of the window above the water, we can use the equation for free fall motion:
h = 0.5 * g * t^2
where:
h is the height above the water,
g is the acceleration due to gravity (approximately 9.8 m/s^2),
and t is the time it takes for the pen to fall.
In this case, the time is given as 2.4 seconds. Substituting these values into the equation, we can solve for h:
h = 0.5 * 9.8 * (2.4)^2
B. Finding the forward distance traveled by the pen:
Since the pen is dropped out of the window, it will inherit the same horizontal velocity as the train. Therefore, we can assume that the horizontal motion of the pen is the same as the train's motion.
The forward distance traveled by the pen can be calculated using the equation:
d = v * t
where:
d is the distance traveled,
v is the velocity of the train (55 m/s),
and t is the time it takes for the pen to fall (2.4 seconds).
Substituting the given values into the equation, we can calculate the forward distance traveled by the pen:
d = 55 * 2.4
So, to summarize:
A. The height of the window above the water can be found using the equation h = 0.5 * g * t^2.
B. The forward distance traveled by the pen can be found using the equation d = v * t.