Ball 1 is launched with an initial vertical velocity v1=160 ft / sec . Three seconds later, ball

step 1 for a ball 1 should take this form. Right? And both balls have the same beginning and ending spo

Ball 1 is launched with an initial vertical velocity v1=160...

Ball 1 is launched with an initial vertical velocity $v_{1}=160 \mathrm{ft} / \mathrm{sec} .$ Three seconds later, ball 2 is launched with an initial vertical velocity $v_{2}$. Determine $v_{2}$ if the balls are to collide at an altitude of $300 \mathrm{ft} .$ At the instant of collision, is ball 1 ascending or descending?

Key Concepts

Projectile Motion

Projectile motion refers to the motion of an object that is launched into the air and moves under the influence of gravity. This concept involves analyzing the object's vertical and horizontal components of motion separately, using gravity as a constant acceleration in the vertical direction. In the context of this problem, only the vertical component is relevant since the balls move vertically.

Kinematic Equations

Kinematic equations describe the motion of objects under constant acceleration. They relate displacement, initial velocity, time, and acceleration. For vertical motion under gravity, these equations allow determination of an object's position and velocity at any point in time, which is essential for analyzing when and where two objects in motion will collide.

Relative Timing and Launch Delays

Relative timing and launch delays are critical when analyzing scenarios involving multiple moving objects that do not start their motion simultaneously. This concept involves adjusting time variables for each object according to their individual start times. In this problem, the delay of three seconds for the second ball's launch must be accounted for to properly synchronize their motions for a collision analysis.

Collision Conditions

The collision condition is met when two objects occupying different motion paths reach the same point in space at the same time. In this context, setting the displacement equations of the two vertically moving balls equal to each other and solving for the unknown parameters (such as the initial velocity of the second ball) ensures that their positions coincide at the collision altitude.

Interpretation of Velocity Direction

Interpreting the sign of the velocity in kinematic calculations helps determine the direction of motion. A positive velocity typically indicates upward motion, while a negative velocity indicates downward motion. This concept is used here to ascertain whether an object is ascending or descending at the point of collision based on its computed vertical velocity.

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