¡¡ remember that the velocity in the Y
(vertical) direction (Vy) is equal to the
V*sin(angle). Remember also that HALF
WAY the vertical velocity is 0. ¿¿
A long jumper leaves the ground at an angle
of 17.8◦ to the horizontal and at a speed of 10.4 m/s.
How far does he jump? The acceleration due to gravity is 9.8 m/s^2.
Answer in units of m.
What maximum height does he reach?
Answer in units of m.
To find the distance the long jumper jumps, we need to calculate the horizontal component of his velocity (Vx) and the time it takes for him to land.
To find Vx, we use the equation Vx = V * cos(angle), where V is the speed (10.4 m/s) and angle is the launch angle (17.8 degrees).
Vx = 10.4 * cos(17.8) = 9.8 m/s
The time it takes for the long jumper to reach the ground is equal to twice the time it takes for the vertical velocity (Vy) to become zero. This is because the Vy starts at 0 m/s, goes up, reaches a maximum, and then comes back down to 0 m/s. So the time it takes for the entire jump is twice the time it takes for the maximum height (halfway) to be reached.
To find the maximum height, we use the equation Vy = V * sin(angle), where V is the speed (10.4 m/s) and angle is the launch angle (17.8 degrees).
Vy = 10.4 * sin(17.8) = 3.0 m/s
Next, we find the time it takes for Vy to become 0 m/s. Since the acceleration due to gravity is acting against the vertical velocity, we can use the equation Vy = g * t, where g is the acceleration due to gravity (9.8 m/s^2) and t is the time.
0 = 9.8 * t
t = 0 seconds (The time taken for Vy to become zero is 0 seconds because the maximum height is reached halfway, meaning the velocity becomes zero at the peak point.)
Now we have the time it takes to reach the maximum height, which is 0 seconds. Since the total time is twice the time to reach the maximum height, the total time is also 0 seconds.
To find the horizontal distance (d), we use the equation d = Vx * t, where Vx is the horizontal velocity (9.8 m/s) and t is the time.
d = 9.8 * 0 = 0 m
Therefore, the long jumper does not jump any horizontal distance, but this is because we assumed there is no air resistance and neglected other factors like the elevation change of the ground.
To find the maximum height, we can use the equation H = (Vy^2) / (2g), where Vy is the vertical velocity (3.0 m/s) and g is the acceleration due to gravity (9.8 m/s^2).
H = (3.0^2) / (2 * 9.8) = 0.46 m
Therefore, the long jumper reaches a maximum height of 0.46 meters.