Hello, Dora!

A ditch 2.5 m wide crosses a trail bike path.

An upward incline of 15° has been built up on the approach

so that the top of the incline is level with the top of the ditch.

What is the minimum speed a trail bike must be moving to clear the ditch?

(Add 1.4 m to the range for the back of the bike to clear the ditch safely.)

Code:

* *
* *
* 15° *
A * - - - - - - - - - - - - - * - - * B
: 2.5 : 1.4 :

The bike is launched at at a 15° angle.

It is to land at point 3.9 meters to the right and at the same height.

The equations of projectile motion are: . v\cos15^o)t \\ y \:= \v\sin15^o)t - 16t^2\end{array}" alt="\begin{array}{cc}x\:=\v\cos15^o)t \\ y \:= \v\sin15^o)t - 16t^2\end{array}" />

. . where is the initial velocity (launch speed).

We want **[1]**

and we want **[2]**

Divide **[2]** by **[1]**: .

Solve for seconds.

From **[1]**, we have: .