Question

A hurdler is 0.535 m from a hurdlewhen he jumps at 6.82 m/s at a 67.9° angle. What is his height when he clears the hurdle?

A) 0.95 m
B) 1.22 m
C) 1.43 m
D) 1.68 m
E) 2.01 m

Answer 1

To find the height when the hurdler clears the hurdle, we need to calculate the vertical component of his velocity when he jumps. Using the given initial velocity and angle, we can calculate the vertical velocity and then use it to find the vertical displacement. The height when the hurdler clears the hurdle is approximately 2.01 m.

Step-by-step explanation:

To find the height when the hurdler clears the hurdle, we need to calculate the vertical component of his velocity when he jumps. We can use trigonometry to do this. The vertical velocity can be found using the equation:

Vertical velocity = initial velocity * sin(angle)

Substituting the given values:

Vertical velocity = 6.82 m/s * sin(67.9°)

Calculating the vertical velocity:

Vertical velocity = 6.82 m/s * 0.920

Vertical velocity ≈ 6.28 m/s

The height when the hurdler clears the hurdle is equal to the vertical displacement. We can calculate the displacement using the equation:

Displacement = vertical velocity * time + 0.5 * acceleration * time^2

Since the hurdler jumps vertically, there is no horizontal displacement and the acceleration is the acceleration due to gravity, which is approximately 9.8 m/s^2. The time can be calculated using the equation:

Time = vertical velocity / acceleration

Substituting the given values:

Time = 6.28 m/s / 9.8 m/s^2

Calculating the time:

Time ≈ 0.64 s

Substituting the calculated values into the displacement equation:

Displacement = (6.28 m/s * 0.64 s) + (0.5 * 9.8 m/s^2 * (0.64 s)^2)

Calculating the displacement:

Displacement ≈ 2.010 m

Therefore, the height when the hurdler clears the hurdle is approximately 2.01 m.