A diver is jumping straight up with 2 m/s from a 15 meter platform. Calculate the maximum height of the diver, the diver’s velocity when reaches the water, and total time to reach the water.
max height: new PE=initial KE
mgh=1/2 mv^2
h= 1/2 v^2/g
velocity at impact
KE at impact= PE lost+ initial KE
1/2 m v^2= mg(15)+1/2 m 2^2
solve for v.
Total time.
hf=hi+vi*t - 4.8t^2
0=15+2t-4.8t^2
solve the quadratic, use the quadratic equation to solve for t.
Thanks bobpursely I need this for my Quantitative Biomechanics class
To solve this problem, we can use the equations of motion to calculate the maximum height, velocity, and total time.
1. Maximum Height:
The maximum height can be found using the equation for vertical motion:
v² = u² + 2as
Given:
Initial velocity (u) = 2 m/s (the speed with which the diver jumps up)
Acceleration (a) = -9.8 m/s² (acceleration due to gravity, always negative when going up)
Since the diver is jumping straight up, the final velocity (v) will be 0 m/s at the maximum height.
Rearranging the equation, we can solve for displacement (s) which represents the maximum height:
s = (v² - u²) / (2a)
Substituting in the given values:
s = (0 - 2²) / (2 * (-9.8))
Calculating the value:
s = - 4 / -19.6
s = 0.204 m
Therefore, the maximum height of the diver is approximately 0.204 meters.
2. Velocity when reaching the water:
To determine the velocity of the diver when reaching the water, we can use the equation:
v = u + at
Given:
Initial velocity (u) = 2 m/s
Acceleration (a) = 9.8 m/s² (since the diver is falling down due to gravity, acceleration is positive)
Time (t) = ?
The time taken for the diver to reach the water can be calculated using the equation:
t = (v - u) / a
Since the final velocity (v) will be unknown, we'll solve for it later.
Now we substitute the known values into the equation:
t = (v - 2) / 9.8
3. Total time to reach the water:
When going up, the acceleration is -9.8 m/s², and when going down, it is +9.8 m/s². Thus, the total time to reach the water is twice the amount of time calculated above.
Total time = 2 * t
Now, let's solve for the unknowns:
To find the final velocity (v), we can use the equation:
v = u + at
Since the diver is reaching the water, the final velocity is 0 m/s. Therefore, we can rewrite the equation as:
0 = 2 + 9.8t
Solving for t:
9.8t = -2
t = -2 / 9.8
Now, substitute the value of t into the total time equation:
Total time = 2 * (-2 / 9.8)
Total time = -4 / 9.8
Total time = 0.408 s
Therefore, the velocity of the diver when reaching the water is 0 m/s, and the total time taken to reach the water is approximately 0.408 seconds.