Problem:  A projectile is fired with speed v0 at an angle θ from the horizontal as shown in the figure below.Part A. Find the highest point in the trajectory, H. Express the highest point in terms of the magnitude of the acceleration due to gravity g, the initial velocity v0, and the angle θ.Part B. What is the range of the projectile, R? Express the range in terms of v0, θ, and g.

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Kinematic equations:

 vf = v0 -gty= (vf+v02)ty= v0t-12gt2 vf2= v02 -2gy

Part A.

From the fourth kinematic equation:

vfy2=v0y2 -2gyy=v0y2-vfy22g

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Problem Details

 A projectile is fired with speed v0 at an angle θ from the horizontal as shown in the figure below.

1. A projectile is fired with speed v0 at an angle

Part A. Find the highest point in the trajectory, H. Express the highest point in terms of the magnitude of the acceleration due to gravity g, the initial velocity v0, and the angle θ.

Part B. What is the range of the projectile, R? Express the range in terms of v0, θ, and g.

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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 Symmetrical Launch concept. You can view video lessons to learn Symmetrical Launch. Or if you need more Symmetrical Launch practice, you can also practice Symmetrical Launch practice problems.

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Based on our data, we think this problem is relevant for Professor Bordel's class at CAL.