Arrow Trajectory: 29° and 50 m/s

[bam3211]

An arrow is shot at 29.0° above the horizontal. Its velocity is 50 m/s and it hits the target.

What is the maximum height the arrow will attain?


The target is at the height from which the arrow was shot. How far away is it?

if anyone could give me some tips or steps to solve this problem that would be great

thanks

 

[ShawnD]

An arrow is shot at 29.0° above the horizontal. Its velocity is 50 m/s and it hits the target.

What is the maximum height the arrow will attain?

Vf^2 = Vi^2 + 2ad

The target is at the height from which the arrow was shot. How far away is it?

How long does the arrow stay in the air? Find that time then multiply it by the horizontal component of the arrow's velocity.


For most (all?) of these gravity related problems, your work should start with the vertical component.

 

[baba89]

To solve this problem, we can use the equations of projectile motion to find the maximum height and distance traveled by the arrow.

First, we can find the initial vertical velocity of the arrow using the given velocity and angle. Using trigonometric functions, we can find that the initial vertical velocity is 50 m/s * sin(29°) = 24.5 m/s.

Next, we can use the equation for maximum height, h = (v^2 * sin^2θ) / (2g), where v is the initial velocity, θ is the angle, and g is the acceleration due to gravity (9.8 m/s^2). Plugging in the values, we get h = (24.5 m/s)^2 * sin^2(29°) / (2 * 9.8 m/s^2) = 20.6 m. Therefore, the maximum height the arrow will attain is 20.6 meters.

To find the distance traveled by the arrow, we can use the equation d = v * cosθ * t, where d is the horizontal distance, v is the initial velocity, θ is the angle, and t is the time. We can find the time by using the equation t = 2 * v * sinθ / g. Plugging in the values, we get t = 2 * 50 m/s * sin(29°) / 9.8 m/s^2 = 5.05 s. Therefore, the distance traveled by the arrow is d = 50 m/s * cos(29°) * 5.05 s = 216.4 m. This means that the target is 216.4 meters away from the point where the arrow was shot.

In summary, the maximum height the arrow will attain is 20.6 meters and the target is 216.4 meters away from the point where the arrow was shot. These calculations assume ideal conditions and do not take into account air resistance or other external factors.