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 38.0° angle. If the shot is made from a horizontal distance of 13.00 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.

a. Find lowest initial speed
b. Find highest initial speed

Answer 1

Given y=2.6-2.1, x1=13-0.22, x2=13+0.22, theta=38 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).