What Speed Is Needed for a Basketball to Reach the Hoop?

• agargento
In summary, the conversation discusses a problem involving a basketball player throwing a ball at a 60° angle above the horizontal to a hoop located 2.8 m away and 0.4 m above the release point. The equations V=V0+at, r(t)=r0+v0t+0.5a2, and V0 x/y=V0sin(θ) are used to solve the problem, but the attempt results in an incorrect answer due to a mistake in substituting values. The expert advises working with symbols and substituting values at the end.
agargento

Homework Statement

A basketball player throws the ball at a 60° angle above the horizontal to a hoop which is located a horizontal distance L = 2.8 m from the point of release and at a height h = 0.4 m above it. What is the required speed if the basketball is to reach the hoop?

Homework Equations

I used V=V0+at and r(t)=r0+v0t+0.5a2
and V0 x/y=V0sin(θ)

The Attempt at a Solution

My attempt: http://i.imgur.com/0vdqdvl.jpg

Got a wrong answer. Would love some guidance. Thanks.

Last edited by a moderator:
**Third question** You write ##0.4 = ... (5.6 V_0 )^2 ## instead of ##0.4 = ... ({5.6 \over V_0}) ^2 ##

A quick check on the dimensions of the last term would have shown that it's not length like the other two.

General advice is to work with symbols and only substitute values at the very last.

BvU said:
**Third question** You write ##0.4 = ... (5.6 V_0 )^2 ## instead of ##0.4 = ... ({5.6 \over V_0}) ^2 ##

A quick check on the dimensions of the last term would have shown that it's not length like the other two.

General advice is to work with symbols and only substitute values at the very last.

Thank you so much! Got the right answer, and definitely will use your advice in the future.

1. What is projectile motion in basketball?

Projectile motion in basketball is the curved path that a basketball follows when it is thrown or shot. It is affected by gravity, air resistance, and the initial velocity of the ball.

2. How does gravity affect projectile motion in basketball?

Gravity is a force that pulls objects toward the center of the earth. In basketball, gravity causes the ball to fall towards the ground, resulting in a curved path. The ball's vertical velocity decreases as it rises, and increases as it falls due to the force of gravity.

3. What is the initial velocity in projectile motion?

The initial velocity is the speed and direction at which an object is launched. In basketball, it refers to the speed and direction at which the ball is thrown or shot. The initial velocity is an important factor in determining the trajectory of the ball.

4. How does air resistance impact projectile motion in basketball?

Air resistance, also known as drag, is the force that opposes the motion of an object through air. In basketball, air resistance slows down the ball as it travels through the air, causing it to have a shorter range and a lower trajectory. This can also affect the accuracy of the shot.

5. Can you calculate the trajectory of a basketball using projectile motion equations?

Yes, the trajectory of a basketball can be calculated using projectile motion equations. These equations take into account factors such as initial velocity, angle of launch, and air resistance to determine the path of the ball. However, in real-life situations, other variables such as the player's technique and external forces may also play a role in the trajectory of the ball.

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