A ditch 2.5 m wide crosses a trail bike path. An upward incline of 15 (degrees) 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 at which 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.)
I don't need the answer, just the work.
2007-12-02 13:21:37 · 1 answers · asked by Anonymous in Science & Mathematics ➔ Physics
When the bike leaves the ground at a 15 degree angle, it is going to rise for a while, reach a peak and come back down. If it is going to clear the ditch, the rear wheel has to be at the level of the ditch edge (its starting point) when it gets there. There is an assumption that the bike position is not going to be distorted by the rider (most of us would throw our bodies upward at the jump to counter the tendency of the bike to pitch down ward.) The center of gravity of the bike will be under the force of gravity from the time the front wheel leaves the ground.
We know the time it takes for the bike to rise and fall x meters under gravity. So that same time must apply to travel 3.9m - 2.5m to get the front wheel over and 1.4m more to get the rear wheel on the other side. The initial velocity upward is the sine of the minimum speed at 15°, The horizontal velocity is the cosine. There are enough equations to solve for the velocity.
2007-12-02 13:37:14 · answer #1 · answered by Mike1942f 7 · 0⤊ 0⤋