A basketball player, standing near the basket to grab a rebound, jumps 73.6 cm vertically. How much time does the player spend in the bottom 15.4 cm of the jump?
I think I have this right, but I'd like someone to make sure.
First I have to find the total time by plugging 73.6 cm (after converting to m) into the equation "x = vt+1/2at^2." Then I have to subtract 15.4 from 73.6 (which is 58.2 cm), and plug that into the same equation.
Finally I subtract the second time from the total time, and that's my answer.
Correct? Yes? No?
No. Using 58.2 cm gives you the time to reach that height. (You will need to use two equations, since V is an unknown also). Subtracting that time from the time it takes to reach 73.6 cm tells you how long you spend in the TOP 15.4 cm of the jump.
Use the height of the jump to solve for V. Then use that V in the equation
x = Vt -(1/2)gt^2 = 0.154 m
to solve for t.
How can I solve for V if I don't yet have the time?
Yes, you're on the right track. To find the time spent in the bottom 15.4 cm of the jump, you need to follow these steps:
1. Convert the distance of the jump from centimeters to meters. Since 1 meter is equal to 100 centimeters, divide 73.6 cm by 100 to get 0.736 meters.
2. Use the equation of motion, x = vt + (1/2)at^2, where x is the vertical distance traveled, v is the initial velocity, t is the time, and a is the acceleration due to gravity (-9.8 m/s^2).
3. To find the total time of the jump, set x as 0.736 m and solve for t. Rearrange the equation to get t^2 + (2v/a)t - (2x/a) = 0, and solve it using the quadratic formula.
4. Once you've found the total time, you need to find the time spent in the bottom 15.4 cm. Convert 15.4 cm to meters by dividing it by 100 (0.154 m).
5. Plug 0.154 m into the equation and solve for t. This will give you the time spent in the bottom 15.4 cm.
6. Finally, subtract the time spent in the bottom 15.4 cm from the total time to get your answer.
So, the steps you described are correct!