Imaging you have to shoot a basketball ball.
The trajectory of the ball will make a basket when x = L and y = Hb
The unknowns are then: F (force to shoot the ball), Vo (the initial velocity of the ball), and t (the time of flight).
Part A (Assignment): Work as a group and find the force (F) to make a basket using Excel to solve the three primary equations simultaneously to find the three unknowns. Use the above given. If possible use the solver function in Excel (see the handouts how to use solver for simultaneous equations).
Part B (Assignment): by trial and error, find the angle that will give the minimum force F to make a basket (hint: try 52 degrees)The trajectory of the ball will make a basket when x = L and y = Hb
The unknowns are then: F (force to shoot the ball), Vo (the initial velocity of the ball), and t (the time of flight).
Part A (Assignment): Work as a group and find the force (F) to make a basket using Excel to solve the three primary equations simultaneously to find the three unknowns. Use the above given. If possible use the solver function in Excel (see the handouts how to use solver for simultaneous equations).
Part B (Assignment): by trial and error, find the angle that will give the minimum force F to make a basket (hint: try 52 degrees)
Hb
Equations of motion :
Ax=0, Ay=32.2
Vx= Vo.cos(α) Vy=Vo.sin(α)- Ay.t
x= Vx.t= Vo.cos(α).t
y= Yo + Vo.sin(α).t - ((Ay.t^2)/2)
Primary three equations are then:
Where (given):
e q n ( 1 ) Vo= sqrt of ( 2/3 .2g.F)
eqn (2) x= Vo.cos(α).t
eqn (3) y= Yo+(Vo.sin(α).t)-((32.2/2)(t^2))
Where (given): Yo= Hs (height of shoot) = 6 ft
α = 70/180 .pi radians
Hb (height of basket) = 12 ft
L ( lenght between shooter and basket)= 20 ft