Question

The greatest height reported for a jump into an airbag is 99.4 m by stuntman Dan Koto. In 1948 he jumped from rest from the top of the Vegas World Hotel and Casino. He struck the airbag at a speed of 39 m/s (88 mi/h). To assess the effects of air resistance, determine how fast he would have been traveling on impact had air resistance been absent.

Answer 1

Answer on Question#54991 – Physics – Mechanics | Kinematics | Dynamics

$$v \approx 44.16 \left(\frac{m}{s}\right) \approx 98.78 \left(\frac{mi}{h}\right)$$

Question

The greatest height reported for a jump into an airbag is $99.4\,m$ by stuntman Dan Koto. In 1948 he jumped from rest from the top of the Vegas World Hotel and Casino. He struck the airbag at a speed of $39\,m/s$ ($88\,mi/h$). To assess the effects of air resistance, determine how fast he would have been traveling on impact had air resistance been absent.

Solution

If case of no effect of air resistance (no dissipation), conservation law holds for this system:

$$mgh = \frac{mv^2}{2},$$

where $m$ – mass of the Dan Koto, $h$ – height of the Vegas World Hotel and Casino, $v$ – speed of the Dan Koto near the airbag, $g$ – gravitational acceleration.

Factor out $v$:

$$v = \sqrt{2gh}$$

Assume that $g \approx 9.81 \left(\frac{m}{s^2}\right)$

Plug in numbers:

$$v = \sqrt{2 * 9.81 * 99.4} \approx 44.16 \left(\frac{m}{s}\right) \approx 98.78 \left(\frac{mi}{h}\right)$$

https://www.AssignmentExpert.com