Concept explainers
Dock diving is a great form of athletic competition for dogs of all shapes and sizes (Fig. P4.33). Sheba, the American Pit Bull Terrier, runs and jumps off the dock with an initial speed of 9.02 m/s at an angle of 25° with respect to the surface of the water. a. If Sheba begins at a height of 0.84 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. c. Determine the peak height above the water reached by Sheba during her jump.
FIGURE P4.33
(a)
The horizontal distance travelled by Sheba before hitting the surface of the water.
Answer to Problem 33PQ
The horizontal distance travelled by Sheba before hitting the surface of the water is
Explanation of Solution
Sheba, the dog, is dock diving in an athletic competition for dogs and jumps off the dock with an initial speed of
Write the formula for the vertical position
Here,
Write the formula for the horizontal position
Here,
Sheba jumped from initial position
The vertical acceleration is due to gravity pulling the Sheba in direction downward,
Substituting
Solving the quadratic equation, the valuable root is
The time taken for Sheba to reach the water surface is
Substitute
Thus, the horizontal distance travelled by Sheba before hitting the surface of the water is
(b)
Write the velocity of Sheba at the instant before she hits the water in component form.
Answer to Problem 33PQ
The velocity of Sheba at the instant before she hits the water in component form is
Explanation of Solution
Write the formula for the velocity vector equation for the projectile motion
Here,
The horizontal velocity component is
The vertical velocity component is
Substituting in equation (III) to find the value of
Thus, the velocity of Sheba at the instant before she hits the water in component form is
(c)
The peak height above the water surface reached by Sheba during her jump.
Answer to Problem 33PQ
The peak height above the water surface reached by Sheba during her jump is
Explanation of Solution
Write the formula for the vertical velocity component for the projectile motion
The initial vertical velocity of Sheba is
Substituting
The time taken for Sheba to reach the peak height is
Substituting
Thus, the peak height above the water surface reached by Sheba during her jump is
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Chapter 4 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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