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 9.52 m/s at an angle of 27° 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 0.78 m above the surface of the water, through what horizontal distance does she travel before hitting the surface of the water?

(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.)

(c) Determine the peak height above the water reached by Sheba during her jump.

Answer 1

To solve this problem you have to know about Projectile motion

Step 1.

Definition: Any object to be released into the air with an initial velocity of arbitrary direction, moves describing a curved path in a plane. A projectile is an object which has communicated an initial velocity and is released to perform a movement under the action of gravity. The projectiles that are closer to Earth following a simple curved path is known as a parabola. To describe the motion is useful to separate it into its horizontal and vertical components.

Step 2.

ANSWER:

a).-

Applying the equation for a projectile motion, the horizontal distance is given for the following equation

,   when R is the horizontal distance, t_f is flight time and v_ox is the horizontal component of velocity

, when g is the gravity, v₀ is the module of velocity and alpha in the angle with horizontal

replace both eauation in the equation of horizontal distance

b).-

c).-

and

The speed v_x is constant in all the path, we can cancel

But Sheba have v_fy zero

If you have any question please let me know in the comments