How fast did you throw the ball in order to get it into the basket?

• Kotune
In summary: Anyways, the equation you're going to want to use is d = v*t+(1/2)a*t2. Having quick equations like altamashghazi suggested is nice, but knowing how to get them is always the best.
Kotune

Homework Statement

You are shooting for a goal in a game of basketball. You throw the ball at an angle of 55° to the horizontal. The basket is 3.0m in front of you and 1.5m above the point where the ball is released. How fast did you throw the ball in order to get it into the basket?

The Attempt at a Solution

u(H) = 3cos55° = 1.72
u(V) = 1.5sin55° = 1.23

u should use the equation:

y=xtanθ-(gx^2)/2(ucosθ)^2

this is the locus of curve of projectile.
θ is the angle of projection from horizontal.

altamashghazi said:
u should use the equation:

y=xtanθ-(gx^2)/2(ucosθ)^2

this is the locus of curve of projectile.
θ is the angle of projection from horizontal.

Hi sorry just a few quick questions. Would x be 3? And what would be the value of u?

Kotune said:
Hi sorry just a few quick questions. Would x be 3? And what would be the value of u?

yes x is 3 and u have to calculate u. this is ur question nah.

altamashghazi said:
u should use the equation:

y=xtanθ-(gx^2)/2(ucosθ)^2

this is the locus of curve of projectile.
θ is the angle of projection from horizontal.

u = 1.5cos 55
= 0.86

y = 3tan(55) - (9.8x3^2) / 2 (0.86cos55)^2
= -172...
Thats not correct.

Kotune said:
u = 1.5cos 55
= 0.86

y = 3tan(55) - (9.8x3^2) / 2 (0.86cos55)^2
= -172...
Thats not correct.
u is initial velocity with which u throw the ball. y=1.5m. .put it in the equation and calculate 'u'

altamashghazi said:
u is initial velocity with which u throw the ball. y=1.5m. .put it in the equation and calculate 'u'

Thanks. How would you arrange it for u?
√1.5 - (3tan(55)) - (9.8x3^2) x (2(cos55)) = u?

Kotune said:
Thanks. How would you arrange it for u?
√1.5 - (3tan(55)) - (9.8x3^2) x (2(cos55)) = u?
solve this it is somewhat lengthy but u will get right answer.
[gx^2/(xtanθ-1.5)]^1/2=ucosθ

Okay, although this problem involves some rather boring and tedious math, the answer is achieved by simply using the kinematic equations as all this is is a projectile motion problem.
Having quick equations like altamashghazi suggested is nice, but knowing how to get them is always the best.

Anyways, the equation you're going to want to use is d = v*t+(1/2)a*t2.

You'll have to split it into components of x and y using 1.5 as d(y) and 3.0 as d(x). Furthermore you'll have to split the velocity which is one of your two unknowns (the other is t) into x and y by multiplying it by cos55 and sin 55. Once you have those filled into the equation as well as the acceleration (hint, there is no acceleration in the x direction, only in the y) then you will have 2 equations and 2 unknowns. Try to solve that yourself.

1. How do you measure the speed of a thrown ball?

The speed of a thrown ball can be measured using a device called a radar gun, which uses Doppler radar to measure the velocity of an object. It works by bouncing radio waves off the moving object and calculating the speed based on the change in frequency of the waves.

2. Does the weight of the ball affect its speed when thrown?

Yes, the weight of the ball can affect its speed when thrown. Generally, a heavier ball will require more force to throw and will therefore have a slower speed compared to a lighter ball. However, other factors such as the shape and aerodynamics of the ball can also play a role in determining its speed.

3. What is the average speed of a thrown basketball?

The average speed of a thrown basketball can vary depending on the force applied by the thrower, the weight and size of the ball, and other external factors such as air resistance. However, on average, a basketball can be thrown at a speed of around 25-30 miles per hour.

4. Can the speed of a thrown ball be increased by using a specific throwing technique?

Yes, the speed of a thrown ball can be increased by using a specific throwing technique, such as using proper body mechanics, applying force from the legs and core, and releasing the ball with a flick of the wrist. These techniques can help increase the velocity of the ball and improve its accuracy when thrown into a basket.

5. What factors can affect the accuracy of a thrown ball?

The accuracy of a thrown ball can be affected by a variety of factors, including the force and angle of the throw, the weight and shape of the ball, air resistance, and external factors such as wind or obstacles. Practice, technique, and muscle memory can also play a role in improving the accuracy of a thrown ball.

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