Solve: (a) upward. (b) downward. (c) 3.65. Set Up: Let be upward. With x and y are related by Solve: (a) when (b) Find x for and gives The quadratic formula gives He lands in the river 28.4 m from the near bank. Reflect: Before doing the calculation for part (b) we don’t know that he landed in the river. If we had found for we would know he hit the vertical face of the far bank before he reached the water. 3.66. Set Up: For the grenade take upward, so Let be the magnitude of the velocity of the grenade relative to the hero. The horizontal range R of the grenade must be 15.8 m plus the distance d that the enemy’s car travels while the grenade is in the air. The enemy’s car is traveling away from the hero’s car with a relative velocity of Solve: with gives gives that The quadratic formula gives The grenade has velocity of magnitude relative to the hero. Relative to the hero the velocity of the grenade has components and Relative to the earth the velocity of the grenade has components and The magnitude of the velocity relative to the earth is 3.67. Set Up: Take downward. Solve: (a) Use the vertical motion to find the time for the boulder to reach the level of the lake: with gives t 5 Å 2 1 y 2 y0 2 a y 5 Å 2 1 20 m 2 9.80 m / s 2 5 2.02 s. y 2 y0 51 20 m y
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