A long jumper leaves the ground at an angle of 15.1◦ to the horizontal and at a speed of 10.9 m/s.
How far does he jump? The acceleration
due to gravity is 9.8 m/s2
.
Answer in units of m
010 (part 2 of 2) 10.0 points
What maximum height does he reach?
Answer in units of m
if you look up trajectory in wikipedia, it gives handy formulas for figuring the height and range of a projectile at a given speed and angle.
But then, you probably already have those formulas, so where do you get stuck?
3.
196m
To find the distance the long jumper jumps, we can use the horizontal motion of the object. Since there is no horizontal acceleration, the horizontal velocity remains constant throughout the jump.
First, let's find the time the jumper is in the air. We can use the vertical motion of the object to find this time. The initial vertical velocity can be calculated using the given speed and the angle of takeoff.
Vertical velocity (V_y) = Initial speed sin(angle)
= 10.9 m/s * sin(15.1°)
Next, we can find the time it takes for the jumper to reach the highest point of their jump. At this point, the vertical velocity becomes zero. We can use the equation for vertical motion under constant acceleration to find this time.
Final vertical velocity (V_yf) = 0 m/s
Initial vertical velocity (V_y) = 10.9 m/s * sin(15.1°)
Acceleration due to gravity (g) = -9.8 m/s^2
Using the formula V_yf = V_y + g * t, we can solve for time (t).
0 = (10.9 m/s * sin(15.1°)) - (9.8 m/s^2 * t)
t = (10.9 m/s * sin(15.1°)) / 9.8 m/s^2
Now that we have the time it takes for the jumper to reach the maximum height, we can find the maximum height using the equation for vertical motion under a constant acceleration.
Initial vertical velocity (V_y) = 10.9 m/s * sin(15.1°)
Acceleration due to gravity (g) = -9.8 m/s^2
Time (t) = (10.9 m/s * sin(15.1°)) / 9.8 m/s^2
Using the formula h = V_y * t - (1/2) * g * t^2, we can solve for the maximum height (h).
Maximum height (h) = (10.9 m/s * sin(15.1°)) * [(10.9 m/s * sin(15.1°)) / 9.8 m/s^2] - (1/2) * 9.8 m/s^2 * [(10.9 m/s * sin(15.1°)) / 9.8 m/s^2]^2
Finally, to find the distance the jumper jumps, we can use the horizontal velocity and the time it takes for the jumper to reach the maximum height. We can use the equation d = V_x * t, where V_x is the horizontal velocity and t is the time.
Horizontal velocity (V_x) = Initial speed cos(angle)
= 10.9 m/s * cos(15.1°)
To find the distance the jumper jumps, we can calculate:
Distance (d) = Horizontal velocity (V_x) * Time (t)
Now you can substitute the given values into these formulas and calculate the distance and maximum height the long jumper reaches.