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?
Ok...after this I swear I'm done!
I just need someone to check my final answer, which is 0.0858 s.
He jumps .736m high, time in air..
time in air falling > 1/2 9.8 t^2=.736
time to fall .763-.154> 1/2 9.8 t2^2=.609
t= sqrt ..736/4.9= .388sec
t2= sqrt.119 = .345s
t-t2= .0434
Now double it for the time going up.
time=.0868 seconds
check my math, we are off on one digit.
See, I use your method without rounding and now come up with 0.0852 s. So...now I'm a little stuck on which answer is the correct one.
To find the time spent in the bottom 15.4 cm of the jump, we can use the equation kinematic equation for vertical motion:
Δy = v0 * t + (1/2) * a * t^2
Where:
Δy is the vertical displacement (73.6 cm - 15.4 cm = 58.2 cm)
v0 is the initial velocity (0 m/s, as the player is at the bottom of the jump)
t is the time spent in the bottom 15.4 cm of the jump
a is the acceleration due to gravity (-9.8 m/s^2)
Plugging in the values:
58.2 cm = 0 m/s * t + (1/2) * -9.8 m/s^2 * t^2
Rearranging the equation, we get t^2 = -2 * (58.2 cm / (-9.8 m/s^2))
t^2 = 117.8776 cm^2 / m^2
t^2 = 0.011963 s^2
Taking the square root of both sides, we get t ≈ 0.1094 s
Therefore, the correct answer is approximately 0.1094 s, not 0.0858 s.
To find the time spent in the bottom 15.4 cm of the jump, we can use the equation of motion for vertical motion:
h = v_initial * t + (1/2) * a * t^2
Where:
- h is the displacement (change in height)
- v_initial is the initial velocity
- a is the acceleration due to gravity (approximately -9.8 m/s^2)
- t is the time
First, we need to convert the given values from centimeters to meters:
- Jump height (h) = 73.6 cm = 0.736 m
- Bottom height (h_bottom) = 15.4 cm = 0.154 m
We need to find the time (t) spent in the bottom 15.4 cm of the jump, so h = h_bottom:
0.154 = v_initial * t + (1/2) * (-9.8) * t^2
Rearranging the equation:
(1/2) * (-9.8) * t^2 + v_initial * t + (h - h_bottom) = 0
Now, we can solve this quadratic equation to find the time spent in the bottom 15.4 cm of the jump. However, you haven't provided the initial velocity (v_initial). Without that information, it is not possible to calculate the time spent in the bottom 15.4 cm of the jump accurately.
So, I'm sorry, but without the initial velocity, I cannot check your final answer or provide you with the correct solution for the time spent in the bottom 15.4 cm.