Question

Alice and Tom dive from an overhang into the lake below. Tom simply drops straight down from the edge, but Alice takes a running start and jumps with an initial horizontal velocity of 25 m/s. Neither person experiences any significant air resistance. Just as they reach the lake below Question 15 options: a) the speed of Alice is larger than that of Tom. b) the splashdown speed of Alice is larger than that of Tom. c) the speed of Tom will always be 9.8 m/s larger than that of Alice. d) the speed of Alice will always be 25 m/s larger than that of Tom. e) they will both have the same speed.

Answer 1

Answer:

$v_f = v_i + a t$

$v_f$ represent the final velocity

$v_i$ represent the initial velocity

a = g = 9.8 m/s2 represent the gravity the only force acting for both

The vertical component of velocity is the same for both since the only force acting on y is the gravity. And we can assume that the horizontal component is constant without acceleration.

So then we have the initial velocities given in the x axis are (0 for John and 25 m/s for Alice). Then we can conclude that the Alice speed is greater. Since

$v = \sqrt{v^2_x +v^2_y}$

a) the speed of Alice is larger than that of Tom

Explanation:

For this case we can use the following kinematic equation:

$v_f = v_i + a t$

$v_f$ represent the final velocity

$v_i$ represent the initial velocity

a = g = 9.8 m/s2 represent the gravity the only force acting for both

The vertical component of velocity is the same for both since the only force acting on y is the gravity. And we can assume that the horizontal component of velocity is the same  for both

So then we have the initial velocities given in the x axis are (0 for John and 25 m/s for Alice). Then we can conclude that the Alice speed is greater. Since

$v = \sqrt{v^2_x +v^2_y}$

Since the component of y is the sam but the componenet for x is greater for Alice the final speed would be higher for Alice.

So then the best option for this case is:

a) the speed of Alice is larger than that of Tom

Answer 2

Answer:

e) they will both have the same speed

Explanation:

Tom simply dropping experiences only vertical motion which is under gravity.

Alice running with an initial horizontal velocity experiences motion in both orientations. However, her vertical motion is still under gravity. Since her initial velocity is purely horizontal, then the initial vertical velocity is 0 m/s, as if she dropped. Hence, she will have the same vertical speed as Tom.

The effect of the horizontal velocity is that she lands farther from Tom but they both land in the same time with the same speed.