You throw a ball straight up with an initial velocity of 15.0 m/s. It passes a tree branch on the way up at a height of 7.00 m. How much additional time will pass before the ball passes the tree branch on the way back down?
The known values are
The applicable formula is .
Using this formula, we can solve it in terms of time, t.
Substituting the known values, we have
We have two values for time, t. These two values represent the times when the ball passes the tree branch. So, the two values of the time, t, are
Therefore, the total time between passing the branch is the difference between 2.49 seconds and 0.57 seconds. That is .
A very strong, but inept, shot putter puts the shot straight up vertically with an initial velocity of 11.0 m/s. How long does he have to get out of the way if the shot was released at a height of 2.20 m, and he is 1.80 m tall?
A dolphin in an aquatic show jumps straight up out of the water at a velocity of 13.0 m/s.
(a) List the knowns in this problem.
(b) How high does his body rise above the water? To solve this part, first note that the final velocity is now a known and identify its value. Then identify the unknown, and discuss how you chose the appropriate equation to solve for it. After choosing the equation, show your steps in solving for the unknown, checking units, and discuss whether the answer is reasonable.
(c) How long is the dolphin in the air? Neglect any effects due to his size or orientation.
The knowns are
At the highest point of the jump, the velocity is equal to 0. That is .
Basing from the known values, the formula that we can use to solve for y is . By rearranging these variables, the formula in solving for is . Therefore we have,
This value is reasonable since dolphins can jump several meters high out of the water. Usually, a dolphin measures about 2 meters and they can jump several times their length.
The formula we can use to solve for the time is . If we rearrange this formula and solve for t, it becomes .
This value is the time it takes the dolphin to reach the highest point. Since the time it takes to reach this point is equal to the time it takes to go back to water, the time it is in the air is .
A rescue helicopter is hovering over a person whose boat has sunk. One of the rescuers throws a life preserver straight down to the victim with an initial velocity of 1.40 m/s and observes that it takes 1.8 s to reach the water. (a) List the knowns in this problem. (b) How high above the water was the preserver released? Note that the downdraft of the helicopter reduces the effects of air resistance on the falling life preserver, so that an acceleration equal to that of gravity is reasonable.