A projectile is launched from ground level at 37.0 m/s at an angle of 30.6 ° above horizontal. Use the launch point as the origin of your coordinate system.
a)How much time elapses before the projectile is at a point 8.9 m above the ground and heading downwards toward the ground?
b)How far downrange (the horizontal distance from the origin) was the projectile when it reached the highest point in its flight?
hf=hi+vi*t-4.9t^2 vi= 37.0*sin30.6 hf=8.9 hi=0 solve for time t.
YOu get two solutions, take the largest time, it is going down then.
Highest point? Vvertical=0
Vv=0=vi*t-4.9t^2 vi = 37*sin30.6
solve for time t.
then horizontal distce= 37cos30.6*time
To solve these problems, we can use the equations of projectile motion. The two main equations we will use are:
1. Vertical displacement equation:
Δy = (V₀y)t + (1/2)gt²
2. Horizontal displacement equation:
Δx = V₀x * t
where:
Δy is the vertical displacement,
V₀y is the initial vertical velocity,
t is the time,
g is the acceleration due to gravity (-9.8 m/s²),
Δx is the horizontal displacement, and
V₀x is the initial horizontal velocity.
Let's solve these parts one by one:
a) How much time elapses before the projectile is at a point 8.9 m above the ground and heading downwards toward the ground?
To find the time elapsed, we need to find the time when the vertical displacement is 8.9 m. In this case, the initial vertical velocity is given as V₀y = V₀ * sin(θ), where V₀ is the initial speed and θ is the launch angle.
We'll plug in the known values into the vertical displacement equation and solve for t:
8.9 = (V₀ * sin(30.6°)) * t + (1/2) * (-9.8 m/s²) * t²
Using the quadratic formula, we can solve for t.
b) How far downrange (the horizontal distance from the origin) was the projectile when it reached the highest point in its flight?
To find the horizontal distance traveled at the highest point in the flight, we need to find the time when the vertical velocity becomes zero (reached the highest point). At this point, the vertical displacement is maximum.
We set V₀y - g * t = 0 and solve for t. Once we have the time, we can use the horizontal displacement equation to find Δx.
Δx = V₀x * t
Now, let's solve these equations to get the answers.