Question

A hurdler is 0.535 m from a hurdle when he jumps at 6.82 m/s at a 6.79 degree angle. What is his height when he clears the hurdle?(Hint: It is not necessarily at the highest point in his motion.) Unit = m. Would love an explanation for this problem!

Answer 1

To find the hurdler's height while clearing the hurdle, split the initial velocity into horizontal and vertical components, calculate the time to reach the hurdle, and then use this time to find the height using the vertical motion equation.

Step-by-step explanation:

To calculate the height a hurdler reaches while clearing the hurdle, we can use the projectile motion equations. Since the asks for the height when clearing the hurdle and it is specified that it's not at the highest point, we only need to find the height at the specific horizontal distance from launch.

Given:

• The initial speed (v) is 6.82 m/s
• The launch angle (θ) is 6.79 degrees
• The horizontal distance (x) from the hurdle is 0.535 m

The horizontal and vertical components of the initial velocity can be found using:

• Vx = v × cos(θ)
• Vy = v × sin(θ)

Since there is no horizontal acceleration, the time (t) to reach the hurdle can be found with:
Vx = x / t => t = x / Vx

Now, we can find the height (y) at time (t) using the vertical motion equation:
y = Vy × t + 0.5 × g × t^2
Here, g is the acceleration due to gravity (9.81 m/s^2, downward).

Since the question hints at not reaching the maximum height, we use the time calculated to reach the horizontal position of the hurdle, and then substrate this time in the vertical motion equation to find the height at this position.