Question

A daredevil on a motorcyclo attempts to clear a 420-meter-wide river from a 210-meter-high cliff. What must his initial horizontal velocity

be?

Answer 1

His initial velocity (speed) must be 64.16 m/s.

Step-by-step explanation:

Horizontal Motion

When an object is horizontally launched at a speed v from a height h, the maximum horizontal distance (also called Range) traveled by the object can be calculated as follows:

`\displaystyle d=v\cdot\sqrt{\frac {2h}{g}}`

Our daredevil is attempting to clear a river d=420 m wide with his motorcycle from a cliff h=210 m high. We need to find the speed needed to safely reach the opposite edge of the river.

From the above equation, we solve for v:

Speed:

`\displaystyle v=d\cdot\sqrt{\frac {g}{2h}}`

`\displaystyle v=420\cdot\sqrt{\frac {9.8}{2\cdot 210}}`

`\displaystyle v=420\cdot\sqrt{\frac {9.8}{420}}`

v = 64.16 m/s

His initial velocity (speed) must be 64.16 m/s.