Projectile motion max height problem

In summary, to find the launch angle for a projectile launched from ground level with an initial speed of 48.7 m/s so that its maximum height is equal to its horizontal range, you can use the high school method with the equations x = vt, Vy = Viy + at, and y = Viy*t - ½at². All three equations are necessary to solve for the unknown variables of time, initial velocity, and angle.
  • #1
dmb325
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Homework Statement



A projectile is launched from ground level with an initial speed of 48.7 m/s. Find the launch angle (the angle the initial velocity vector is above the horizontal) such that the maximum height of the projectile is equal to its horizontal range. (Ignore any effects due to air resistance.)

Homework Equations



Vocos(angle)=Vx
Vosin(angle)=Vy


The Attempt at a Solution


(X, 0) and (X/2, Ymax)
 
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  • #2
In my experience you can always solve these projectile motion questions with the high school method. Write x = vt for the horizontal part,
Vy = Viy + at AND y = Viy*t - ½at² for the vertical part.
In this problem you need all three equations because you have unknown t, Vi and the angle. Give it a try!
 

1. What is projectile motion?

Projectile motion is the motion of an object that is launched into the air and then moves along a curved path due to the influence of gravity. It is a combination of horizontal and vertical motion.

2. How do you calculate the maximum height of a projectile?

The maximum height of a projectile can be calculated using the formula h = (v2sin2θ) / 2g, where v is the initial velocity, θ is the angle of projection, and g is the acceleration due to gravity.

3. What factors affect the maximum height of a projectile?

The maximum height of a projectile is affected by the initial velocity, angle of projection, and acceleration due to gravity. Other factors such as air resistance and wind can also have an impact.

4. Can a projectile reach an infinite height?

No, a projectile cannot reach an infinite height. Due to the influence of gravity, the object will eventually reach a maximum height and then fall back down to the ground.

5. How does the maximum height of a projectile change with different initial velocities and angles?

The maximum height of a projectile will increase with a higher initial velocity and a larger angle of projection. However, if the angle is too high, the object will not travel as far horizontally and will also have a shorter flight time.

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