On level ground a shell is fired with an initial velocity of 40.0 m/s at 60.0° above the horizontal and feels no appreciable air resistance. How long does it take the shell to reach its highest point?

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Identify the vertical component of the initial velocity. Use the formula: \( v_{0y} = v_0 \sin(\theta) \), where \( v_0 = 40.0 \text{ m/s} \) and \( \theta = 60.0^\circ \).

Recognize that at the highest point, the vertical velocity is zero. Therefore, use the kinematic equation: \( v_y = v_{0y} - g t \), where \( v_y = 0 \) and \( g = 9.8 \text{ m/s}^2 \) (acceleration due to gravity).

Rearrange the kinematic equation to solve for time \( t \): \( t = \frac{v_{0y}}{g} \).

Substitute the expression for \( v_{0y} \) from step 1 into the equation from step 3.

Calculate the time \( t \) using the values obtained from the previous steps, ensuring all units are consistent.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Projectile Motion

Projectile motion refers to the motion of an object thrown or projected into the air, subject to only the acceleration of gravity. It involves two components of motion: horizontal and vertical. The horizontal motion is uniform, while the vertical motion is uniformly accelerated, typically due to gravity.

Initial Velocity Components

The initial velocity of a projectile can be broken down into horizontal and vertical components using trigonometry. For a velocity v at an angle θ, the horizontal component is v*cos(θ) and the vertical component is v*sin(θ). These components are crucial for analyzing the projectile's motion separately in each direction.

Time to Reach Maximum Height

The time to reach the maximum height in projectile motion is determined by the vertical component of the initial velocity and the acceleration due to gravity. At the highest point, the vertical velocity becomes zero. The time can be calculated using the formula t = (v*sin(θ))/g, where g is the acceleration due to gravity.