Physics Kinematics Example
A ball is thrown upward from the ground with an initial speed of 25 m/s; at the same instant, another ball is dropped from a building 15 m high. After how long will the balls be at the same height?
To solve this problem, consider the motion of both balls separately. The first ball is thrown upward from the ground, and its vertical position changes as it moves upward, slows down, and eventually comes back down. The second ball, dropped from a height of 15 meters, starts with an initial velocity of zero and accelerates downward due to gravity.
For the ball thrown upward, you need to calculate how its height changes over time based on its initial speed and how gravity slows it down. For the ball dropped from the building, its height decreases steadily due to gravity pulling it down. The goal is to find the moment when both balls are at the same height by setting their vertical positions equal to each other and solving for the time.
Related Problems
A ball is thrown off a building. If the ball is thrown up at 5 m/s and lands 3 seconds later
Find the height of the building
Find the impact velocity of the ball
A key falls from a bridge that is 45 m above the water. It falls directly onto a model boat moving with constant velocity that is 12 m in front of the point of impact when the key is released. What is the speed of the boat?
A swimmer is capable of swimming 0.60 ni/s in still water. (a) If she aims her body directly across a 55-m-wide river whose current is 0.50 m/s, how far downstream (from a point opposite her starting point) will she land? (b) How long will it take her to reach the other side?
In a rescue attempt, a hovering helicopter drops a life preserver to a swimmer being swept downstream by a river current of a constant velocity v. The helicopter is at a height of 9.8 m. The swimmer is 6.0 m upstream from a point directly under the helicopter when the life preserver is released. It lands 2.0 m in front of the swimmer. How fast is the current flowing? Neglect air resistance.
13.7 m/s
9.8 m/s
6.3 m/s
2.8 m/s