Question

Dock diving is a great form of athletic competition for dogs of all shapes and sizes. Sheba, the American Pit Bull Terrier, runs and jumps off the dock with an initial speed of 8.72 m/s at an angle of 28

∘
with respect to the surface of the water. (Assume that the +x axis is in the direction of the run and the +y axis is up.) (a) If Sheba begins at a height of 0.85 m above the surface of the water, through what horizontal distance does she travel before hitting the surface of the water? m (b) Write an expression for the velocity of Sheba, in component form, the instant before she hits the water. (Express your answer in vector form.
v
=m/s (c) Determine the peak height above the water reached by Sheba during her jump. m

Answer 1

Initial velocity of Sheba, v = 8.72 m/s

Angle of jump, θ = 28°

We can use the following kinematic equations of motion to solve the problem:

v = u + at

s = ut + (1/2)at^2

v^2 = u^2 + 2as

where,

u = initial velocity (m/s)

v = final velocity (m/s)

a = acceleration (m/s^2)

t = time (s)

s = displacement (m)

Let's assume that Sheba jumps horizontally off the dock and neglect the air resistance. In this case, the vertical component of the velocity will be zero.

Horizontal component of the velocity, v_x = v * cosθ

Vertical component of the velocity, v_y = v * sinθ = 0 (Neglecting the air resistance)

Now, we can use the horizontal component of the velocity to find out the time taken by Sheba to hit the water.

Time taken by Sheba to hit the water, t = (2 * v_x) / a

Since the vertical component of the velocity is zero, the displacement of Sheba in the vertical direction will be:

s_y = (1/2) * a * t^2

Substituting the values, we get:

v_x = v * cosθ = 8.72 * cos28° = 7.842 m/s

a = 9.81 m/s^2 (acceleration due to gravity)

t = (2 * v_x) / a

= (2 * 7.842) / 9.81

= 1.58 s (approx)

s_y = (1/2) * a * t^2

= (1/2) * 9.81 * (1.58)^2

= 12.22 m (approx)

Therefore, the time taken by Sheba to hit the water is approximately 1.58 seconds and the displacement of Sheba in the vertical direction is approximately 12.22 meters.

Step-by-step explanation: