What Are the Launch Angles for Half the Maximum Range of a Projectile?

In summary, a projectile range question is a physics problem that involves calculating the distance traveled by an object launched into the air. The formula for calculating projectile range is R = (v^2 * sin(2θ)) / g, where R is the range, v is the initial velocity, θ is the angle of launch, and g is the acceleration due to gravity. The range is affected by the initial velocity and angle, with higher values resulting in a longer range and lower values resulting in a shorter range. The range will always be a positive value and is typically measured in meters (m).
  • #1
mullets1200
14
0

Homework Statement


A projectile's horizontal range on level ground is R =v0^2 sin2(theta)/g. At what launch angle or angles will the projectile land at half of its maximum possible range.


The Attempt at a Solution



So what i did was:
Half the range occurs when sin(2θ) = 0.5

So 2θ = arcsin(0.5)...so θ = 0.5*arcsin(0.5) = 15 (degrees)

but when i enter that in it says there is more than one answer, how do i get the other answer?
 
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  • #2
If sin (alpha)=0.5, alpha can be 30 or 180-30 degrees.

ehild
 

FAQ: What Are the Launch Angles for Half the Maximum Range of a Projectile?

What is a projectile range question?

A projectile range question is a type of physics problem that involves calculating the distance traveled by an object (the projectile) that is launched into the air with a certain initial velocity and angle.

What is the formula for calculating projectile range?

The formula for calculating projectile range is R = (v^2 * sin(2θ)) / g, where R is the range, v is the initial velocity, θ is the angle of launch, and g is the acceleration due to gravity.

How is the range affected by the initial velocity and angle?

The range is directly proportional to the square of the initial velocity and the sine of twice the angle of launch. This means that increasing the initial velocity or angle will result in a longer range, while decreasing them will result in a shorter range.

Can the range be negative?

No, the range cannot be negative. It represents the distance traveled by the projectile, so it will always be a positive value.

What is the unit of measurement for projectile range?

The unit of measurement for projectile range is typically meters (m), since it represents a distance.

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