In an action-adventure film, the hero is supposed to throw a grenade from his ca
ID: 1962607 • Letter: I
Question
In an action-adventure film, the hero is supposed to throw a grenade from his car, which is going 89.0 km/h, to his enemy's car, which is going 124 km/h. The enemy's car is 15.0 m in front of the hero's when he lets go of the grenade.
A)If the hero throws the grenade so its initial velocity relative to him is at an angle of 45 degree 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.
answer: ____in km/h please im totally stuck dont even know how to start from ur solution i can learn how to do the steps
B)Find the magnitude of the velocity relative to the earth.
answer: ____k'h
Explanation / Answer
The velocity of the hero car, u = 89.0 km/h The velocity of the enemy's car, v = 124 km/h The separtion between both cars, d0 = 15.0 m ___________________________________________________________ A) The horizontal distance traveled by the grenade relative to the hero is R = d0+v't ...... (1) Here, the velocity of the enemy relative to the hero is v' = 124 km/h-89.0 km/h = 35 km/h = (35)(0.2778) m/s = 9.723 m/s The horizontal distance also be written as R = voxt t = R/v0x Therefore, the equation (1) becomes R = d0+v'(R/v0x) ....... (2) ____________________________________________________________ Using kinematic relations, the horizontal range is R = v02sin2/g Here, the angle = 45o Thus, R = v02sin2(45o)/g (since, sin90o = 1) = v02/g ...... (3) ____________________________________________________________ The x-component of the velocity v0 is v0x= v0cos45o (since, cos45o = 1/2) = v0/2 ...... (4) ____________________________________________________________ The equation (2), becomes [v02/g] = d0+v'([v02/g]/[ v0/2]) v02= d0g+2v'v0 Thus, Thus, v02 - 2v'v0 -d0g = 0 v02 - 2(9.723 m/s)v0 -(15.0 m)(9.8 m/s2) = 0 v02 - 13.75v0 -147 = 0 Solve the above quadratic equation, we get v0 = 20.813 m/s = (20.813 m/s)(1 km/h/0.2778 m/s) = 74.92 km/h Therefore, the velocity of the grenade relative to the hero is 74.92 km/h. Therefore, the velocity of the grenade relative to the hero is 74.92 km/h. NOTE: v0 = 75 km/h (approximately) ______________________________________________________________ ______________________________________________________________ B) The x-component of the velocity of the grenade relative to the hero is v0x' = v0cos45o = (74.92 km/h)cos45o = 52.976 km/h The y-component of the velocity of the grenade relative to the hero is v0y' = v0sin45o = (74.92 km/h)sin45o = 52.976 km/h The x-component of the velocity of the grenade relative to the earth is v0x'' = 52.976 km/h+89.0 km/h = 141.976 km/h The y-component of the velocity of the grenade relative to the earth is v0y'' = 52.976 km/h _____________________________________________________________________ The magnitude of the velocity of the grenade relative to the earth is v = (141.976 km/h)2+(52.976 km/h)2 = 151.54 km/h = (74.92 km/h)cos45o = 52.976 km/h The y-component of the velocity of the grenade relative to the hero is v0y' = v0sin45o = (74.92 km/h)sin45o = 52.976 km/h The x-component of the velocity of the grenade relative to the earth is v0x'' = 52.976 km/h+89.0 km/h = 141.976 km/h The y-component of the velocity of the grenade relative to the earth is v0y'' = 52.976 km/h _____________________________________________________________________ The magnitude of the velocity of the grenade relative to the earth is v = (141.976 km/h)2+(52.976 km/h)2 = 151.54 km/h v0y' = v0sin45o = (74.92 km/h)sin45o = 52.976 km/h The x-component of the velocity of the grenade relative to the earth is v0x'' = 52.976 km/h+89.0 km/h = 141.976 km/h The y-component of the velocity of the grenade relative to the earth is v0y'' = 52.976 km/h _____________________________________________________________________ The magnitude of the velocity of the grenade relative to the earth is v = (141.976 km/h)2+(52.976 km/h)2 = 151.54 km/h = (74.92 km/h)sin45o = 52.976 km/h The x-component of the velocity of the grenade relative to the earth is v0x'' = 52.976 km/h+89.0 km/h = 141.976 km/h The y-component of the velocity of the grenade relative to the earth is v0y'' = 52.976 km/h _____________________________________________________________________ The magnitude of the velocity of the grenade relative to the earth is v = (141.976 km/h)2+(52.976 km/h)2 = 151.54 km/h v0y'' = 52.976 km/h _____________________________________________________________________ The magnitude of the velocity of the grenade relative to the earth is v = (141.976 km/h)2+(52.976 km/h)2 = 151.54 km/h = 151.54 km/hRelated Questions
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