You must have seen actors in Hindi films jumping over huge gaps on horse backs and motor cycles. In this problem consider a daredevil motor cycle rider trying to cross a gap at a velocity of 100 km h–1. (Fig. 4.13). Let the angle of incline on either side be 450. Calculate the widest gap he can cro

1 answer

I dont get your angle of incline b eing 450?

lets call it theta.
initial vertical speed=100km/hr*1hr/3600sec*1000m/km(*sinTheta=27.7(sinTheta) m/s
initial horizontal speed=27.7(cosTheta)

At the widest gap, he will land at the edge (barely), so jump distance=horizontal speed*timeinair.
timeinair: Hf=hi+vi'cosTheta*time-1/2 g time^2
or time(vi-4.9t)=0 or timeinair= 27.7*sinTheta*/4.9 check that.
widest gap= 27.7*cosTheta*27.7*sinTheta/4.9
if you wish, you can convert sin*cos to another angle using the addition formula, but i see no advantage to doing so.. Note the max width will occur at 45 deg