Projectile Motion Ball Hurl Question

In summary, the range equation for throwing a ball with initial speed 30m/s is d = v0^2sin2θ/g. To achieve maximum range, the angle θ must be 45 degrees. The maximum value for sin2θ is 1, which results in the widest river you can throw the ball across being 900m.
  • #1
yoyo16
35
0

Homework Statement



If you can hurl a ball so that its initial speed is 30m/s, what is the widest river you can throw it across?

Homework Equations


The range equations,
t=2(vi)(sintheta)/g

d=visin2theta/g


The Attempt at a Solution



I know you have to use components so what I got what Vx=30sintheta and Vy=30costheta

I don't know what to do next or how to sub it in because there isn't a angle given . Can someone please help me. Thanks
 
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  • #2
You have your formula for the range as

[tex]d = \frac{v_i sin2 \theta}{g}[/tex]

For you to throw it at the max range, you'd need to throw it such that your angle θ and hence sin2θ is maximum.

What is the maximum value that sin2θ can be?
 
  • #3
rock.freak667 said:
You have your formula for the range as

[tex]d = \frac{{v_{0}}^2 sin2 \theta}{g}[/tex]

For you to throw it at the max range, you'd need to throw it such that your angle θ and hence sin2θ is maximum.

What is the maximum value that sin2θ can be?

Forgot a square!
 
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  • #4
The angle must be 45 degrees to get max range right?
 
  • #5
Oh ok, I got the answer. Thanks so much !
 

Related to Projectile Motion Ball Hurl Question

1. What is projectile motion?

Projectile motion is the motion of an object through the air that is influenced by gravity and has a constant horizontal velocity. It follows a curved path known as a parabola.

2. How is projectile motion different from regular motion?

Regular motion is the motion of an object that is not influenced by external forces, while projectile motion is affected by gravity. This means that the object will follow a curved path rather than a straight line.

3. How is the horizontal and vertical motion of a projectile related?

The horizontal and vertical motion of a projectile are independent of each other. This means that while the object is moving horizontally at a constant velocity, it is also accelerating vertically due to the force of gravity. The two motions combine to create the curved path of the projectile.

4. What factors affect the trajectory of a projectile?

The trajectory of a projectile is affected by the initial velocity, the angle at which it is launched, and the force of gravity. Air resistance can also play a role in altering the trajectory.

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

Projectile motion has many real-life applications, such as in sports like baseball or golf, where the trajectory of the ball is crucial for scoring. It is also used in engineering for designing and launching rockets, missiles, and other projectiles. In addition, it can be used in physics experiments to study the effects of gravity and motion.

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