In an action-adventure film, the hero is supposed to throw a grenade from his ca

Question

In an action-adventure film, the hero is supposed to throw a grenade from his car, which is going 70.0 km/h, to his enemy's car, which is going 113 km/h. The enemy's car is 16.3 m in front of the hero's when he lets go of the grenade. Part A If the hero throws the grenade so its initial velocity relative to him is at an angle of 45degree above the horizontal, what should the magnitude of the initial velocity be? The cars are both traveling in the same direction on a level road. You can ignore air resistance.

Explanation / Answer

it will be easy if we solve this with reletive motion

so let the hero's car is at rest

so enemy' car speed ( with resppect to hero's car) = (113-70) km/h

= 43 km/h = 11 .94 m/s

now this is projectile motion with velocity lets( say u )and at angle of 45 degree from horizontal and the distance b/w both cars in starting is 16.3 m

if the grenade must hit the enemy's car then in t sec time ( t = flight time of granade)

(distance traveled by enemy car) + 16.3 = range of granade

( t * 11.94) + 16.3 = u cos45 *t ........(1)

where t = 2( u sin45)/g ....(2)

now from both equations

11.94 *2( u sin45)/g +16.3 = ucos45 *2( u sin45)/g

u = 23.64 m/s = 85.01 km/h ( with respect to hero's car )

so wrt the ground = 85.01 + 70 = 155.01 km/h

answer

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