Answer Q40 and Q42 Using Motion Near the Surface of Eerth. Formaul Field Goal A

Question

Answer Q40 and Q42

Using Motion Near the Surface of Eerth. Formaul

Field Goal A kicker for a football team is attempting a field goal from a distance of 40 yards (120 feet) away from the goal post. The ball is kicked from the ground with an initial velocity of 65 feet per second and at an initial angle of 40degree. Will the ball clear the goal post bar, which is 10 feet above the ground! Assume gravity is the only force acting on the object. Out at Home A baseball is thrown from center field at an initial height of 5 feet and with an initial angle of 30degree. The ball reaches the catcher's glove 200 feet away and 1 foot above the ground without a bounce. What was the initial velocity of the ball. assuming gravity was the only force acting on it?

Explanation / Answer

Q 40) velocity in horizontal direction = 65*cos40 = 49.79 ft/s

time to reach 120 ft = 120/49.79 = 2.41 s {there is no acceleration in horizontal direction}

velocity in y- dir = 65*sin40 = 41.78 ft/s

at 2.41 s , vertical positon of ball = 41.78*2.41 - 0.5*32.174*2.41^2 = 7.25 ft which is less than 10 ft

=> ball will not be able to clear the goal post.

Q 42) let initial velocity be v

horizontal velocity = v*cos30 = 0.866v

time taken to reach 200 ft = 200/0.866v = 230.94/v

verical velocity = v*sin30 = 0.5v

as the final vertical position is 4 fts below the initial position.

-4 = (0.5v)*(230.94/v) - 0.5*32.174*(230.94/v)^2

v = 84.74 ft/s

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