🎡AP Physics 1
4. In Scenario 1, a student standing on the ground throws a ball horizontally with an initial speed of v₀ = 8.0 m/s from a height of h = 2.0 m above the ground, as shown in Figure 1. The ball lands on the ground a horizontal distance d₁ from the point directly below where it was released. Air resistance is negligible.
Figure 1. Ball thrown horizontally
Figure 2. Cart and ball motion
Indicate whether d₁ is greater than, less than, or equal to d₂ by writing one of the following in your answer booklet.
• d₁ > d₂
• d₁ < d₂
• d₁ = d₂
Justify your answer in terms of ALL components of the ball's motion as observed from the ground reference frame in each scenario (see Figure 1 and Figure 2). Use qualitative reasoning beyond referencing equations.
Starting with kinematic principles, derive an expression for the horizontal distance d the ball travels before landing on the ground. Express your answer in terms of vₓ, h, and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information. Consider the general case where a ball is thrown horizontally with an initial horizontal velocity component vₓ from a height h above the ground.
Indicate whether the expression for the distance d you derived in part B is or is not consistent with the claim made in part A. Briefly justify your answer by referencing your derivation in part B and the relationship between the horizontal velocity components in the two scenarios as observed from the ground reference frame.
