A long jumper leaves the ground at an angle of 25.2 to the horizontal and at a speed of
11.2 m/s.
How far does he jump? The acceleration
due to gravity is 9.8 m/s2 .
Answer in m
What maximum height does he reach?
Answer in units of m
1. Dh = Vo^2*sin(2A) / g,
Dh = (11.2)^2*sin50.4 / 9.8 = 9.86m.
2. Yo = ver. = 11.2sin25.2 = 4.77m/s.
h = (Yf^2 - Yo^2) / -19.6,
h = (0 - (4.77)^2) / -19.6 = 1.161m
To find the distance the long jumper jumps, we can decompose the initial velocity into horizontal and vertical components.
1. Horizontal component: The horizontal velocity remains constant throughout the jump. So, we can use the formula: distance = velocity × time. Since the time is the same for both horizontal and vertical components, we can use the given speed (11.2 m/s) and angle (25.2°) to find the horizontal component:
horizontal velocity = speed × cos(angle)
2. Vertical component: The vertical motion can be analyzed using the equations of motion. The initial vertical velocity is given by the speed (11.2 m/s) multiplied by the sine of the angle:
vertical velocity = speed × sin(angle)
We need to find the time taken by the jumper to reach the maximum height, as the maximum height occurs when the vertical velocity becomes zero.
Using the formula for vertical displacement, we have:
vertical displacement = vertical velocity × time + 1/2 × acceleration × time²
Since the vertical displacement at maximum height is zero, we can use this equation to find the time taken to reach the maximum height.
Once we have the time taken to reach the maximum height, we can use it to find the total time of flight by doubling it.
Finally, to find the horizontal distance jumped, we multiply the horizontal velocity by the total time of flight.
Let's calculate:
1. Horizontal component:
horizontal velocity = 11.2 m/s × cos(25.2°)
2. Vertical component:
vertical velocity = 11.2 m/s × sin(25.2°)
3. Time taken to reach the maximum height:
Use the equation for vertical displacement:
0 = vertical velocity × time + 1/2 × acceleration × time²
Solving for time, we get:
time = -2 × vertical velocity / acceleration
4. Total time of flight:
total time = 2 × time
5. Horizontal distance jumped:
distance = horizontal velocity × total time
Now you can substitute the values into these formulas to find the answers.