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https://texercises.com/exercise/initial-speed-for-basketball-throw/
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Exercise:
A basketball leaves a player's hands at a height of .m above the floor. The basket is .m above the floor. The player likes to shoot the ball at a ang. angle. If the shot is made from a horizontal distance of .m and must be accurat to pm.m horizontally what is the range of initial speeds allowed to make the basket?

Solution:
The ball is glqq goodgrqq if he is thrown within a distance of .m dots .m. Two s determine each motion of a thrown object: h fracgt^+v_y t fracgt^ + v_ sinalpha t s_x v_x t v_ cosalpha t Since we do neither know the duration t of the throw nor the initial velocity v_ we can't work with only one of them. Eliminating the time t which is not explicitly of erest by subsituting it in one with the expression obtained from the other we up with: h fracgt^ + v_ sinalpha t fracgleftfracs_xv_xright^ + v_ sinalpha leftfracs_xv_xright fracgleftfracs_xv_ cosalpharight^ + v_ sinalpha leftfracs_xv_ cosalpharight fracg fracs_x^v_^cos^alpha + s_xtanalpha Solved for the initial speed v_ we get: v_ sqrtfracgs_x^cos^alphafracs_x tanalpha - h v_.m .meterpersecond v_.m .meterpersecond The basketball player has to shoot the ball within a speed range of .meterpersecond dots .meterpersecond.
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Exercise:
A basketball leaves a player's hands at a height of .m above the floor. The basket is .m above the floor. The player likes to shoot the ball at a ang. angle. If the shot is made from a horizontal distance of .m and must be accurat to pm.m horizontally what is the range of initial speeds allowed to make the basket?

Solution:
The ball is glqq goodgrqq if he is thrown within a distance of .m dots .m. Two s determine each motion of a thrown object: h fracgt^+v_y t fracgt^ + v_ sinalpha t s_x v_x t v_ cosalpha t Since we do neither know the duration t of the throw nor the initial velocity v_ we can't work with only one of them. Eliminating the time t which is not explicitly of erest by subsituting it in one with the expression obtained from the other we up with: h fracgt^ + v_ sinalpha t fracgleftfracs_xv_xright^ + v_ sinalpha leftfracs_xv_xright fracgleftfracs_xv_ cosalpharight^ + v_ sinalpha leftfracs_xv_ cosalpharight fracg fracs_x^v_^cos^alpha + s_xtanalpha Solved for the initial speed v_ we get: v_ sqrtfracgs_x^cos^alphafracs_x tanalpha - h v_.m .meterpersecond v_.m .meterpersecond The basketball player has to shoot the ball within a speed range of .meterpersecond dots .meterpersecond.
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Attributes & Decorations
Asked Quantity
Branches
Kinematics
Tags
basketball, free, freier fall, kinematics, mechanics, physics, throw, trajectory
Difficulty
(4, default)
Points
3 (default)
Language
ENG (English)
Type
Calculative / Quantity
Decoration
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