Question

A BMX biker leaves the end of a horizontal ledge with a velocity of 27 m/s and lands 7.2 m from the base of the ledge. How high is the ledge?

Answer 1

To find the height of the ledge, we can use the equations of motion. The horizontal distance covered by the biker can be related to the time of flight and the horizontal velocity. Since the biker starts at ground level with zero initial vertical velocity, the vertical displacement is equal to the height of the ledge.

Step-by-step explanation:

To find the height of the ledge, we can use the equations of motion. The horizontal distance covered by the biker can be related to the time of flight and the horizontal velocity using the equation:

Distance = Velocity * Time

Since the vertical motion is affected by gravity, we can use the equations of motion in the vertical direction:

Vertical Displacement = Initial Vertical Velocity * Time + 0.5 * Acceleration * Time^2

Since the biker starts at ground level with zero initial vertical velocity, the vertical displacement is equal to the height of the ledge.

Given:
Initial Horizontal Velocity (u) = 27 m/s
Horizontal Distance (d) = 7.2 m
Vertical Acceleration due to Gravity (g) = 9.8 m/s^2

Using the equation Distance = Velocity * Time, we can rearrange it to solve for time:

Time = Distance / Velocity

Substituting the given values:
Time = 7.2 m / 27 m/s = 0.2667 s

Using the equation Vertical Displacement = Initial Vertical Velocity * Time + 0.5 * Acceleration * Time^2, we can rearrange it to solve for the initial vertical velocity:

Initial Vertical Velocity = (Vertical Displacement - 0.5 * Acceleration * Time^2) / Time

Substituting the given values:
Initial Vertical Velocity = (0 - 0.5 * 9.8 m/s^2 * (0.2667 s)^2) / 0.2667 s = -1.28 m/s

Since the biker leaves the ledge with an upward vertical velocity, the magnitude of the initial vertical velocity is 1.28 m/s. Therefore, the height of the ledge is 1.28 m.

Answer 2

Given data

*The given velocity of the BMX biker is u = 27 m/s

*The horizontal range from the base of the ledge is R = 7.2 m

The formula for the time taken by the BMX bike is to reach 7.2 m from the base of the ledge is given by the relation as

`\begin{gathered} R=ut \\ t=(R)/(u) \end{gathered}`

Substitute the known values in the above expression as

`\begin{gathered} t=(7.2)/(27) \\ =0.26\text{ s} \end{gathered}`

The formula for the height of the ledge is given by the equation of motion as

`h=(1)/(2)gt^2`

Substitute the known values in the above expression as

`\begin{gathered} h=(1)/(2)*9.8*(0.26)^2 \\ =0.33\text{ m} \end{gathered}`

Hence, the height of the ledge is h = 0.33 m