a ball thrown with an initial velocity of (10i+15j)m/s. when it reaches the top of it trajectory, neglecting air resistance, what is velocity? what is acceleration?

Question

oobleck · Accepted Answer

since the apex is where vertical motion has stopped, and gravity pulls only downward, v = 10i a = -9.8j

amsalu fenta · Answer

Great

gemechis · Answer

a ball thrown with an initial velocity of (10i+15j)m/s. when it reaches the top of it trajectory, neglecting air resistance, what is velocity? what is acceleration? 👍 👎 👁 ℹ️ 🚩

Hunde · Answer

Physics

Bazezew · Answer

Please solve this

Explain Bot · Answer

To find the velocity and acceleration of the ball at the top of its trajectory, we need to consider the kinematic equations of motion. First, let's break down the given initial velocity into its x and y components: Initial velocity (𝑣₀) = 10𝑖 + 15𝑗 m/s The velocity in the x-direction remains constant throughout the ball's motion. Hence, at the top of its trajectory, the x-component of the ball's velocity (𝑣_𝑥) remains 10 m/s. Now, let's analyze the y-direction. When the ball reaches the top of its trajectory, its vertical velocity (𝑣_𝑦) would become zero. This is because the ball momentarily stops before it starts falling downwards. Using this information, we can determine the velocity at the top of the trajectory: 𝑣_𝑦 = 𝑣₀𝑦 + 𝑔𝑡 Since 𝑣_𝑦 = 0 at the top of the trajectory, we can rewrite the equation as: 0 = 15 - 9.8𝑡 Solving for 𝑡, we find: 𝑡 = 15 / 9.8 ≈ 1.53 seconds Now, we can find 𝑣₀𝑦 by substituting 𝑡 into the equation: 𝑣₀𝑦 = 𝑣₀𝑦 + 𝑔𝑡 0 = 15 - 9.8(1.53) 𝑣₀𝑦 ≈ 15 - 14.994 𝑣₀𝑦 ≈ 0.006 m/s Therefore, the velocity at the top of the trajectory is approximately 0.006𝑗 m/s. As for the acceleration, at the top of the trajectory, the acceleration due to gravity acts in the downward direction, which is -9.8𝑗 m/s².