An Olympic long jumper is capable of jumping 7.5 m. Assume that his horizontal speed is 8.8 m/s as he leaves the ground.
How long is he in the air?
How high does he go? Assume that he lands standing upright, that is, the same way he left the ground.
Dx = Xo*t = 7.5 m.
8.8 * t = 7.5.
t = 0.852 s.
h = 0.5g*t^2.
g = 9.8 m/s^2.
t = 0.852 s.
h = ?.
To find out how long the long jumper is in the air, we can use the formula for time:
Time = Displacement / Velocity
In this case, the displacement is the horizontal distance the jumper covers, which is 7.5 m. The velocity is the horizontal speed at which the jumper leaves the ground, which is 8.8 m/s.
Time = 7.5 m / 8.8 m/s
Calculating this, we find that the long jumper is in the air for approximately 0.852 seconds.
Now, let's determine how high the long jumper goes. To solve this, we'll need to find the vertical distance covered during the jump. However, we do not have the initial vertical velocity or the time of flight.
To find the initial vertical velocity, we need to know the time it takes for the jumper to reach the peak of their jump. The time to reach the peak can be found using the equation:
Time_to_peak = (Final_velocity - Initial_velocity) / Acceleration
Since we know the final velocity at the peak is 0 m/s (the moment when the jumper changes direction), and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the time it takes to reach the peak.
Time_to_peak = (0 m/s - ?) / -9.8 m/s^2
To find the initial vertical velocity, we can use the equation:
Displacement = Initial_velocity * Time + (1/2) * Acceleration * Time^2
The displacement at the peak is equal to the vertical distance covered by the jumper during the jump. We know the displacement is 0 since the jumper lands at the same height as they take off. The time we use here is half of the total time of flight since the jumper spends an equal amount of time going up and coming down.
0 = ? * (0.852 seconds / 2) + (1/2) * -9.8 m/s^2 * (0.852 seconds / 2)^2
Solving this equation will give us the initial vertical velocity.
Once we have the initial vertical velocity, we can calculate the maximum height using the equation:
Maximum_height = (Initial_velocity^2) / (2 * Acceleration)
Finally, plugging in the calculated values, we can determine the maximum height reached by the jumper.