I already know theanswer (58.6 km/h) but I want to know how to work it out for t

Question

I already know theanswer (58.6 km/h) but I want to know how to work it out for thefuture... thanks In an action-adventure film, the hero is supposed to throw agrenade from his car, which is going 84.0 {rm km/h}, to his enemy's car,which is going 100 {rm km/h}. The enemy's caris 16.6 {rm m} in front of the hero'swhen he lets go of the grenade. If the hero throwsthe grenade so its initial velocity relative to him is at an angleof 45 ^circ above the horizontal, whatshould the magnitude of the initial velocity be? The cars are bothtraveling in the same direction on a level road. You can ignore airresistance I already know theanswer (58.6 km/h) but I want to know how to work it out for thefuture... thanks

Explanation / Answer

100 km/hr = 27.78 m/s = V2 84 km/hr = 23.33 m/s = V1 R = (V2 - V1) t + 16.6   whereR is the range of the projectile R = v2 / g    the range (maximumrange) of a projectile at 45 deg v2 / g = 4.45 R / vx +16.6    wherevx  = v cos45      thehorizontal component of the projectile's speed Substitute and simplify v2 - 6.293 v - 162.6 = 0 v = 16.3 m/s = 58.7 km/hr

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