what should the magnitude of the initial velocity be? The cars are both travelin

Question

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.

Alternative Exercise 3.105 Part A In an action-adventure film, the hero is supposed to throw a grenade from his car, which is going 77.0 km/h, to his enemy's car, which is going 105 km/h.The enemy's car is 13.6 m in front of the hero's when he lets go of the grenade. If the hero throws the grenade so its initial velocity relative to him is at an angle of 45 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. to = km/h Submit My Answers Give Up Part B Find the magnitude of the velocity relative to the earth. 0 s20 km/h Submit My Answers Give Up

Explanation / Answer

Here,

convert velocities into m/s;

77km/h = 77*1000/3600 = 21.39 m/s

105km/h = 105*1000/3600 = 29.167 m/s

The velocity of the enemy's car is

29.167 - 21.39 = 7.77m/s

And the grenade is released with the launch angle 45.

After the grenade is released it is moving according to the equations of projectile motion. Along axis x there is motion with constant velocity:

x(t) = v * cos 45*t

Along axis y there is motion with constant acceleration:

y(t) = v* sin 45*t - 0.5*9.8*t^2

vy(t) = v * sin - 9.8*t

The equation of enemy's car motion:

xenemy(t) = 13.6 + 7.77*t

At some moment of time t0 the x coordinate of grenade should be equation to the x-coordinate of enemy's car and

at the same moment the y cordinates of grenade be zero;

0 = v * sin (45) t0 - 0.5 * 9.8 * t0^2

x(t0) = v * cos (45)*t0 = xenemy(t0) = 13.6 + 7.77 *t0

v * sin 45 = 0.5 * 9.8 * t0

v * cos (45)t0 = 13.6 + 7.77*t0

t0 = 0.144 * v

v * cos (45)0.144*v = 13.6 + 7.77*0.144*v

v = 18.29 m/s

This is the velocity of the grenade relative to the hero.

The x-component of this velocity is 18.29 * cos(45) + 21.39 = 34.3230 m/s

The y component is 18.29 * sin(45) = 12.93 m/s

The magnitude is (34.3230^2 + 12.93^2)^1/2 = 36.678 m/s

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