A broad jumper begins his jump at an angle of 22 f degrees from the horizontal at the middle of the jump he reaches a height of 70m
ANSWER: 9.16m/s
Relevant Formulas: dv=1/2at^2...dh=vht...t=vv/a..
To find the speed at the middle of the jump, we can use the formula: final velocity (vf) = initial velocity (vi) + acceleration (a) × time (t).
Since the jumper starts from rest (vi = 0) and we want to find the speed at the middle of the jump, we need to find the time it takes for the jumper to reach the middle of the jump.
To find the time (t), we can use the formula: vertical displacement (dh) = initial vertical velocity (viy) × time (t) + 1/2 × acceleration due to gravity (g) × time^2.
Given that the jumper reaches a height of 70m at the middle of the jump, the vertical displacement (dh) is 70m. We also know that the initial vertical velocity (viy) is 0 (since the jumper starts from rest) and the acceleration due to gravity (g) is approximately 9.8 m/s^2.
Using the formula for vertical displacement, we can rearrange the equation to solve for time (t):
70 = 0 × t + 1/2 × 9.8 × t^2
Simplifying the equation:
70 = 4.9 × t^2
Dividing both sides by 4.9:
t^2 = 70 / 4.9
Taking the square root of both sides to solve for t:
t = √(70 / 4.9) ≈ 3.09 seconds
Now that we have the time (t), we can find the speed (vf) at the middle of the jump using the formula:
vf = vi + a × t
Since the initial velocity (vi) is 0 and the acceleration (a) is the acceleration due to gravity (-9.8 m/s^2), we have:
vf = 0 + (-9.8) × 3.09
Solving for vf:
vf ≈ -30.28 m/s
However, the speed must be positive, so we take the absolute value:
vf ≈ 30.28 m/s
Therefore, the speed at the middle of the jump is approximately 30.28 m/s.