1. Questions

Physics based Calculus

Bob has just finished climbing a sheer cliff above a beach, and wants to figure out how high he climbed. All he has to use, however, is a baseball, a stopwatch, and a friend on the ground below with a long measuring tape. Bob is a pitcher, and knows that the fastest he can throw the ball is 86.0 mph. Bob starts the stopwatch as he throws the ball (with no way to measure the ball\'s initial trajectory), and watches carefully. The ball rises then and then falls, and after 0.910 seconds the ball is once again level with Bob. Bob can\'t see well enough to time when the ball hits the ground. Bob\'s friend then measures that the ball landed 453 ft from the base of the cliff. How high up is Bob, if the ball started from exactly 5 ft above the edge of the cliff?

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
Brianna

  1. height of ball above cliff is

    h = 5 + vy*t - 16t^2

    assuming vy is y-component of maximum speed of 86 mph = 126.13 ft/s

    h = 0 after .910 sec, so
    vy = 9.1 ft/s

    now, vy^2 + vx^2 = v^2
    9.1^2 + vx^2 = 126.13^2
    vx = 125.8 ft/s

    ball fell from cliff height
    453/125.8 = 3.6 sec

    after falling back to cliff height, the distance fallen to ground was

    9.1t + 16t^2 = 241 ft

    so, the cliff is 241 ft high

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
    Steve

Respond to this Question

First Name

Your Response

Similar Questions

  1. Language Arts

    1. Which of the following transitions shows a comparison? A. although B. however C. just as** D. whereas 2. Which answer option best revises the sentences for transition use? Sentence: You can get to the beach by car. You can ride

  2. physics

    A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of 18m/s. The cliff is 50m above a flat horizontal beach, as shown in Figure 3.20. How long after being released does the stone

  3. Algebra

    A beach ball rolls off a cliff and onto the beach. The height, in feet, of the beach ball can be modeled by the function h(t)=64–16t2, where t represents time, in seconds. What is the average rate of change in the height, in

  4. physics

    A 0.33- kg pendulum bob is attached to a string 1.2 m long and hangs vertically as shown in Figure 1. What is the change in the pendulum bob’s gravitational potential energy as it swings from the lowest point of the pendulum to

  1. physics

    A daring 510 { N} swimmer dives off a cliff with a running horizontal leap, as shown in the figure below. What must her minimum speed be just as she leaves the top of the cliff so that she will miss the ledge at the bottom, which

  2. physics

    A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of 16.0 m/s. The cliff is h = 25.0 m above a flat horizontal beach, as shown in the figure below. How long after being released

  3. physics

    if a ball is thrown horizontally from the top of a cliff and takes 3 seconds to reach the beach below. calculate the height of the cliff by considering the vertical motion only. answer : s=ut+half at(square) s=0*3+half*10*3 s=3+45

  4. physics

    A rock is thrown from a cliff top at 18m/s, 25 degrees above the horizontal. It lands on the beach 4.2 seconds later. a) What is the height of the cliff? b) Hor far from the base of the cliff did the rock land?

  1. physics

    A cannon, located 60.0 m from the base of a vertical 25.0 -m-tall cliff, shoots a 15-kg shell at 43.0 degrees above the horizontal toward the cliff. (a) What must the minimum muzzle velocity be for the shell to clear the top of

  2. Physics

    Bob has just finished climbing a sheer cliff above a beach, and wants to figure out how high he climbed. All he has to use, however, is a baseball, a stopwatch, and a friend on the ground below with a long measuring tape. Bob is a

  3. Physics

    The pendulum bobs in the figure are made of soft clay so that they stick together after impact. The mass of bob B is 14 times that of bob A. Bob B is initially at rest. If bob A is released from a height h above its lowest point,

  4. physics

    A projectile is launched straight up at 54.5 m/s from a height of 88 m, at the edge of a sheer cliff. The projectile falls, just missing the cliff and hitting the ground below. (a) Find the maximum height of the projectile above

View more similar questions or ask a new question.