Projectile Motion that ends before max. distance

In summary, the problem involves a basketball being shot from a height of 2.1 m to a basket 2.6 m above the floor at a 38° angle from horizontal. The question asks for the initial speed of the basketball, given that the shot is made from a distance of 11.22 meters. The equations used to solve this problem include the relationship between velocity, displacement, and acceleration, as well as the maximum distance and maximum height formulas for projectiles. After trying various approaches, the solution is found by first finding the speed and angle at which the ball reaches a height of 2.6 m, and then using the formula for maximum distance.
  • #1
Mambo
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Homework Statement


A basketball leaves a player's hands at height of 2.1 m above floor. the basket is 2.6 m above the floor, player shoots the ball at a 38° angle from horizontal. if the shot is made from a distance of 11.22 meters what is initial speed?
answer is 11 m/s

Homework Equations


v^2=iv^2+2ad (i: initial, v: velocity, d: displacement, a: acceleration)
d=ivt+.5a(t^2) (t: time)
a=(v-iv)/t
max distance=(iv^2 sin2θ)/9.8
max height=(iv^2 sin^2(θ))/(2*9.8)

The Attempt at a Solution


i have tried using 11m as max distance just in case, but did not get desired answer.
thought a lot about using max height, but there are two variables.
i feel like there is just one piece of data missing, but unfortunately there is not.
also, i can get the rates at which some variables are equal to each other, but i do not see it helping in any manner.
i have literally been unable to do this for nearly 1 and a half hours.
 
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  • #2
Welcome to PF.
first find the speed angle with horizontal when ball reaches the height of 2.6 meter then apply the formula of maximum distance. It should work.
Do you know why i say to find the velocity and angle at the time when it is at height of 2.6 meter.(see proof of maximum distance of projectile)
 

1. How is projectile motion defined?

Projectile motion is the motion of an object through the air under the influence of gravity. It is characterized by a combination of horizontal and vertical motion.

2. What causes projectile motion to end before reaching its maximum distance?

The main factor that causes projectile motion to end before reaching its maximum distance is air resistance. As the object moves through the air, it experiences a force in the opposite direction of its motion, causing it to slow down and eventually stop.

3. How does the angle of launch affect projectile motion?

The angle of launch plays a crucial role in determining the path and range of a projectile. A higher angle of launch will result in a higher peak height and shorter range, while a lower angle of launch will result in a lower peak height and longer range.

4. Can projectile motion be accurately predicted?

Yes, projectile motion can be accurately predicted using mathematical equations such as the kinematic equations and Newton's laws of motion. However, factors such as air resistance and wind can affect the accuracy of these predictions.

5. What are some real-world applications of projectile motion that ends before reaching its maximum distance?

Some examples of real-world applications of projectile motion that ends before reaching its maximum distance include sports such as baseball, golf, and javelin throwing. It is also important in understanding the trajectory of objects launched from a slingshot or catapult.

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