Question

flying circus of physics
the current world - record motorcycle jump is 77.0 m, set by jason renie. assume that he left the take - off ramp at 11.0° to the horizontal and that the take - off and landing heights are the same. neglecting air drag, determine his take - off speed.
number
units

Explanation:

Step1: Recall range formula for projectile

The range \(R\) of a projectile (when take-off and landing heights are equal) is given by:
$$R = \frac{v_0^2 \sin(2\theta)}{g}$$
where \(v_0\) is take-off speed, \(\theta\) is launch angle, \(g = 9.81\ \text{m/s}^2\) is gravitational acceleration.

Step2: Rearrange for \(v_0\)

Isolate \(v_0\) by rearranging the formula:
$$v_0 = \sqrt{\frac{Rg}{\sin(2\theta)}}$$

Step3: Substitute given values

Given \(R = 77.0\ \text{m}\), \(\theta = 11.0^\circ\):
First calculate \(2\theta = 22.0^\circ\), \(\sin(22.0^\circ) \approx 0.3746\)
$$v_0 = \sqrt{\frac{77.0 \times 9.81}{0.3746}}$$
$$v_0 = \sqrt{\frac{755.37}{0.3746}} \approx \sqrt{2016.47}$$

Answer:

\(44.9\ \text{m/s}\)