# What have I done wrong? (projectile motion)

• Mayzu
In summary: If your calculations are right so far, you're just a step away from the answer. sin2θ is 2sinθcosθ.
Mayzu

## Homework Statement

A cricketer fields the ball in the outfield, some 80 meters from the wicket keeper. The fielder needs to return the ball to the wicket keeper as quickly as possible. He can throw the ball with a speed of 140 km/hr. The cricket ball has a mass of 0.0168kg
(e) The fielder decides to throw the ball straight back to the wicket keeper, 80 m away. At what angle to the horizontal must he project the ball so that the ball reaches the wicket keeper without hitting the ground?

This question is worth 8 marks, but I cannot figure out how to do it!

Vf=Vi+a(delta)t

## The Attempt at a Solution

http://imgur.com/OJEDalz

^here's my working out. I just can't get past the last step, and my graphics calculator can't either, making me think I'm doing it completely wrong.

Mayzu said:

## Homework Statement

A cricketer fields the ball in the outfield, some 80 meters from the wicket keeper. The fielder needs to return the ball to the wicket keeper as quickly as possible. He can throw the ball with a speed of 140 km/hr. The cricket ball has a mass of 0.0168kg
(e) The fielder decides to throw the ball straight back to the wicket keeper, 80 m away. At what angle to the horizontal must he project the ball so that the ball reaches the wicket keeper without hitting the ground?

This question is worth 8 marks, but I cannot figure out how to do it!

Vf=Vi+a(delta)t

## The Attempt at a Solution

http://imgur.com/OJEDalz

^here's my working out. I just can't get past the last step, and my graphics calculator can't either, making me think I'm doing it completely wrong.

Where does the number 38.9 come from in your work?

I think the right approach is to key in on Vy=0 at 40m, and use the time from that equation to help the rest of your calculations...

berkeman said:
Where does the number 38.9 come from in your work?

I think the right approach is to key in on Vy=0 at 40m, and use the time from that equation to help the rest of your calculations...
38.9 is the initial velocity of the ball. That's what I've done, but I'm stuck...

Mayzu said:

## Homework Statement

A cricketer fields the ball in the outfield, some 80 meters from the wicket keeper. The fielder needs to return the ball to the wicket keeper as quickly as possible. He can throw the ball with a speed of 140 km/hr. The cricket ball has a mass of 0.0168kg
(e) The fielder decides to throw the ball straight back to the wicket keeper, 80 m away. At what angle to the horizontal must he project the ball so that the ball reaches the wicket keeper without hitting the ground?

This question is worth 8 marks, but I cannot figure out how to do it!

Vf=Vi+a(delta)t

## The Attempt at a Solution

http://imgur.com/OJEDalz

^here's my working out. I just can't get past the last step, and my graphics calculator can't either, making me think I'm doing it completely wrong.
Are both of them (the players) assumed to be just two points? Shouldn't their heights be taken into account? In that case, you could use 38.9 as initial velocity (resultant) and put that in the range formula to get sin2θ. That value of θ would be the critical one, means just enough to make the ball reach the ground.

Last edited:
Mayzu said:

## Homework Statement

A cricketer fields the ball in the outfield, some 80 meters from the wicket keeper. The fielder needs to return the ball to the wicket keeper as quickly as possible. He can throw the ball with a speed of 140 km/hr. The cricket ball has a mass of 0.0168kg
(e) The fielder decides to throw the ball straight back to the wicket keeper, 80 m away. At what angle to the horizontal must he project the ball so that the ball reaches the wicket keeper without hitting the ground?

This question is worth 8 marks, but I cannot figure out how to do it!

Vf=Vi+a(delta)t

## The Attempt at a Solution

http://imgur.com/OJEDalz

^here's my working out. I just can't get past the last step, and my graphics calculator can't either, making me think I'm doing it completely wrong.
If your calculations are right so far, you're just a step away from the answer. sin2θ is 2sinθcosθ..

## 1. What is projectile motion?

Projectile motion refers to the movement of an object through the air or space under the influence of gravity. It is a combination of horizontal and vertical motion, and is affected by factors such as initial velocity, angle of launch, and air resistance.

## 2. What are common mistakes people make when calculating projectile motion?

One common mistake is not taking into account air resistance, which can significantly affect the trajectory of the object. Another mistake is forgetting to convert units (e.g. from feet to meters) when using equations. It is also important to ensure that the initial velocity and angle of launch are accurate.

## 3. How do you calculate the maximum height and range of a projectile?

To calculate the maximum height of a projectile, you can use the equation h = (v0 sinθ)^2 / 2g, where v0 is the initial velocity and θ is the angle of launch. To calculate the range, you can use the equation R = v0^2 sin2θ / g.

## 4. Can a projectile's motion be affected by factors other than gravity?

Yes, a projectile's motion can also be affected by air resistance and wind. Air resistance can alter the trajectory and speed of the projectile, while wind can change the direction of the projectile's motion.

## 5. How can projectile motion be applied in real life?

Projectile motion has many practical applications, such as in sports like baseball and golf, where players must consider the angle and force of their swing to achieve the desired trajectory. It is also used in engineering and physics to calculate the trajectory of objects like rockets and satellites.

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