A cannonball is fired with an initial velocity of 20 m / s and a launch angle of 45^∘ at a wall

step 1 This problem we have given a cannon ball is fired with an initial velocity which is 20 meter per

A cannonball is fired with an initial velocity of 20 m / s...

A cannonball is fired with an initial velocity of 20 $\mathrm{m} / \mathrm{s}$ and a launch angle of $45^{\circ}$ at a wall 30 $\mathrm{m}$ away. If the cannonball just barely clears the wall, what is the maximum height of the wall? (A) 5.92 $\mathrm{m}$ (B) 6.34 $\mathrm{m}$ (C) 7.51 $\mathrm{m}$ (D) 8.32 $\mathrm{m}$

A cannonball is fired with an initial velocity of 20 $\mathrm{m} / \mathrm{s}$ and a launch angle of $45^{\circ}$ at a wall 30 $\mathrm{m}$ away. If the cannonball just barely clears the wall, what is the maximum height of the wall?
(A) 5.92 $\mathrm{m}$
(B) 6.34 $\mathrm{m}$
(C) 7.51 $\mathrm{m}$
(D) 8.32 $\mathrm{m}$

Key Concepts

Time Determination in Projectile Motion

Determining the time it takes for a projectile to reach a certain horizontal distance involves dividing that distance by the horizontal component of the initial velocity. This time is crucial for evaluating the projectile’s vertical position and ensuring it reaches desired heights.

Trigonometry in Motion

Trigonometry is fundamental in analyzing projectile motion as it provides the tools to split an initial velocity vector into its horizontal and vertical components, which are then used in further kinematic calculations.

Kinematics Equations

Kinematics equations describe the relationship between displacement, velocity, time, and acceleration. They are used separately in the horizontal direction (with constant velocity) and the vertical direction (with constant acceleration due to gravity) in projectile problems.

Initial Velocity Decomposition

Decomposing the initial velocity into horizontal and vertical components using sine and cosine functions is essential. This involves using trigonometric functions to determine the contributions of the initial speed in both the x and y directions.

Projectile Motion

Projectile motion involves the motion of an object thrown or projected into the air, subject only to the acceleration of gravity. It is characterized by a curved trajectory determined by independent horizontal and vertical motions.

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