In this problem, we're asked to calculate the initial speed, given the horizontal distance travelled and the initial and final directions of motion.
For projectile motion problems in general, we'll follow these steps to solve:
The four UAM (kinematics) equations are:
We define our coordinate system so that the +y-axis is pointing upwards and the +x-direction is horizontal along the launch direction. That means ay = −g, and ax = 0 (because the only acceleration acting on a projectile once it's launched is gravity.)
For a horizontally launched projectile, we also know that v0y = 0.
Finally, we might need to know how to decompose a velocity vector into its x- and y-components:
Or how to get the magnitude and angle of a velocity vector if we know the components:
Step 1. The problem gives us the horizontal distance the arrow traveled and the angle of its final velocity, as well as the fact that it's shot horizontally. So our known, unknown, and target variables are as follows:
In the x-direction:
i. v0x = ?
ii. Δx = 61.0 m
iii. ax = 0 m/s2
iv. vfx = ?
v. t = ?
You are watching an archery tournament when you start wondering how fast an arrow is shot from the bow. Remembering your physics, you ask one of the archers to shoot an arrow parallel to the ground. You find the arrow stuck in the ground 61.0 m away, making a 3.00° angle with the ground.
How fast was the arrow shot?
Frequently Asked Questions
What scientific concept do you need to know in order to solve this problem?
Our tutors have indicated that to solve this problem you will need to apply the Projectile Motion: Horizontal & Negative Launch concept. If you need more Projectile Motion: Horizontal & Negative Launch practice, you can also practice Projectile Motion: Horizontal & Negative Launch practice problems.