Physics with Calc 1 - 6.A Boston Celtics basketball player who is 2.00 m tall is
ID: 1434133 • Letter: P
Question
Physics with Calc 1 -
6.A Boston Celtics basketball player who is 2.00 m tall is standing on the floor L = 9.00 m from the basket, as in Figure P4.54. If he shoots the ball at a 37.0° angle with the horizontal, at what initial speed must he throw so that it goes through the hoop without striking the backboard? The basket height is 3.05 m. Hints: The ending height is not the same as the starting height, so you cannot use the range or time of flight formulas. Decompose the motion into x and y components. Using the x-component of the motion, write an expression that relates v0 and t. Then do the same for the y-component of motion. You should then have two equations for the two unknowns v0 and t.
Explanation / Answer
PROJECTILE
1)
along horizantal
initial velocity vox = vo*costheta
ax = 0
from equaiton of motion
x = vox*T+ 0.5*ax*T^2
x = vo*costheta*T
T = x/(vo*costheta)......(1)
along vertical
voy = vo*sintheta
acceleration ay = -g = -9.8 m/s^2
displacement y = -30 m
from equation of motion
dy = voy*T + 0.5*ay*T^2
dy = (vo*sintheta*x)/(vo*costhetra) - (0.5*g*x^2)/(vo^2*(costheta)^2)
dy = x*tantheta - ((0.5*g*x^2)/(vo^2*(costheta)^2))
(3.05-2) = (9*tan37)-(0.5*9.8*9^2/(v0^2*(cos37)^2))
vo = 10.42 m/s <<<<<------answer