Posted by Pat on .
I have two different questions I can't figure out.
1) Projectile motion: At what initial speed must the basketball player throw the ball at an angle of 55 degrees above the horizontal, to make the foul shot? The horizontal distance from the ball to the basket is 13 feet. Initial height of the ball is 7 ft and the final height which is the basket is 10 ft.
2)Force and Motion: A 12 kg armadillo runs onto a large pond of level, frictionless ice. The armadillo's initial velocity is 5m/s along the positive direction of the x-axis. Take its initial position on the ice as being the origin. It slips over the ice while being pushed by a wind with a force of 17N in the positive direction of the y-axis. In unit vector notation, what are the animal's (a) velocity and (b) position vector when it has slid for 3 seconds?
Physics (#1 of 2) -
Assume 10 ft is the top of the trajectory. (Acually, a good free throw shooter would aim higher than that.) The ball must rise 3 feet in the time it takes to travel horizontally 13 feet. Let T be the travel time from release until it is at the basket. Let V be the release velocity.
Vcos55*T = 13 ft
Vsin55 = g T where g is the acceleration of gravity, 32.2 ft^2/s.
tan 55 = gT^2/13
T^2 = (13/32.2)tan55 = 0.577 sec^2
T = 0.759 sec
Now solve for V