A basketball leaves a player's hands at a height of 2.10 m above the floor. The basket is 2.60 m above the flo

Question

A basketball leaves a player's hands at a height of 2.10 m above the floor. The basket is 2.60 m above the floor. The player likes to shoot the ball at a 37.5° angle. If the shot is made from a horizontal distance of 12.50 m and must be accurate to 0.22 m (horizontally), what is the range of initial speeds allowed to make the basket? Enter your answer to at least four significant digits.

lowest initial speed __ m/s
highest initial speed __ m/s

Answer 1

Given y=2.6-2.1, x1=12.5-0.22, x2=12.5+0.22, theta=37.5 deg, find v0. From the ref., in a ballistic trajectory,
t = x/(v0*cos(theta); y = v0*t*sin(theta) - g*t^2/2
Substitute RHS of t eqn. in y eqn.:
y = x*tan(theta) - g*x^2/(2*v0^2*cos(theta)^2)
y = x*tan(theta) - g*x^2*(1+tan(theta)^2)/(2*v0^2) (trig. identity)
v0 = sqrt(x*tan(theta) - g*x^2*(1+tan(theta)^2)/(2*y))
Solve this for givens (with both values of x).