Drew drops a cherry pit out the car window 1.0 m above the ground while traveling down the road at 18 m/s.
(a) How far, horizontally, from the initial dropping point will the pit hit the ground?
(b) Draw or describe a picture of the situation.
(c) If the car continues to travel at the same speed, where will the car be in relation to when the pit lands?
They probably expect you to ignore air resistance, but in the real world it would have a large effect upon where a cherry pit lands. You are talking about 65 miles per hour.
If you choose to ignore air resistance, multiply 18 m/s by the time it takes to drop one meter.
Yiug
To solve this problem, we can use the equations of motion to find the horizontal distance the cherry pit will travel before hitting the ground.
(a) To find the horizontal distance, we need to determine the time it takes for the cherry pit to hit the ground. We can use the equation:
h = ut + (1/2)gt^2
Where:
h = height (1.0 m)
u = initial velocity in the vertical direction (0 m/s, since the cherry pit is dropped)
g = acceleration due to gravity (-9.8 m/s^2, assuming upward as positive)
t = time
Since the cherry pit is dropped, its initial vertical velocity is 0 m/s. Therefore, the equation simplifies to:
h = (1/2)gt^2
Rearranging the equation, we get:
t^2 = (2h / g)
Substituting the values, we have:
t^2 = (2 * 1.0 / 9.8)
t^2 ≈ 0.204
t ≈ √0.204
t ≈ 0.452 s
Now, to find the horizontal distance, we can use the equation:
s = ut
Since there is no horizontal acceleration, the horizontal velocity remains constant at 18 m/s throughout. Therefore:
s = (18 m/s) * (0.452 s)
s ≈ 8.136 m
Thus, the cherry pit will hit the ground approximately 8.136 meters horizontally from the initial dropping point.
(b) To describe the picture of the situation, you can visualize a car moving horizontally along a road while a cherry pit is dropped from a height of 1.0 meter out of the car's window. The cherry pit will follow a curved path due to the downward force of gravity and eventually hit the ground at a certain horizontal distance from the initial dropping point.
(c) If the car continues to travel at the same speed, it will be 8.136 meters ahead of the point where the cherry pit lands.