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Question Video: Calculating the Vertical Displacement of a Projectile Physics • 9th Grade

A projectile is fired at an angle of 32° above the horizontal with an initial speed of 44 m/s. What is the maximum upward vertical displacement of the projectile from its launch position?

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Video Transcript

A projectile is fired at an angle of 32 degrees above the horizontal with an initial speed of 44 meters per second. What is the maximum upward vertical displacement of the projectile from its launch position?

Okay, so, let’s say that this is ground level and this orange line shows us the trajectory of this projectile. The projectile is fired at an initial speed we’ll call 𝑣 sub 𝑖 and at an angle we’ll call 𝜃. We want to solve for the maximum upward vertical displacement the projectile reaches, that is, this displacement here. We’ll call it ℎ sub max.

Since we’re working with a projectile and we know its initial speed and direction of travel, we can recall an equation for the maximum height reached by a projectile in terms of its initial speed and its direction. Since we’re given 𝑣 sub 𝑖 and 𝜃 and we also know that the acceleration due to gravity is 9.8 meters per second squared, we can plug these values into our equation for ℎ sub max. When we enter this expression on our calculator, to two significant figures, we find a result of 28 meters. This is the maximum vertically upward displacement of our projectile.

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