Math

a light shines from the top of a pole 50ft high. a ball is dropped from the same height from a point 30 ft away from the light. how fast is the ball's shadow moving along the ground 1/2 sec later? (assume the ball falls at a distance of s=16t^2 in t sec)

  1. 👍
  2. 👎
  3. 👁
  1. when the ball is at height h, the shadow is at distance x from the base of the light pole. Using similar triangles,

    x/50 = (x-30)/h
    h = 50(x-30)/x = 50 - 1500/x

    now, h = 50-s = 50-16t^2, so
    dh/dt = -32t, and
    h(1/2) = 50 - 16(1/4) = 46
    x/50 = (x-30)/46, so x=375

    -32t = 1500/x^2 dx/dt
    at t = 1/2,
    -16 = 1500/(140625) dx/dt
    dx/dt = -1500

    so, the shadow is moving toward the pole at 1500 ft/s

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. algebra

    Two vertical poles 20m and 30m high are 60m apart.A rope is to be attached from the top of one pole to a point on the ground halfway between the poles and then to the top of the other pole.How long a rope is needed?

  2. geometry

    Two vertical poles 20 meterd and 30 metrrd high, are 60 meters apart. A rope is to be attached from the top of one pole to a point on the ground half-way between the poles and then to the top of other pole. How long a rope is

  3. Trigonometry

    A vertical pole 35m high, standing on sloping ground is braced by a wire which extends from the top of the pole to a point on the ground 25 m from the foot of the pole. If the pole subtends an angle of 30 degrees at the point

  4. Calculus

    A street light is at the top of a 17 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 6 ft/sec along a straight path. How fast is her shadow lengthening when she is 30 ft from the base of the pole?

  1. physics

    A ball is thrown horizontally at 10.0 m/s from the top of a hill 50.0 m high. How far from the base of the hill would the ball hit the ground? I don't understand the following explained by Quittich (sp)? "Since there is no

  2. Physics

    A ball is dropped from the top of a building. If it takes 3.00 s for the ball to hit the street below, how high is the building?

  3. physics

    a ball is dropped from the top on an 80-m high building. what speed does the ball have in falling 3.5 s?

  4. Physics

    A stone dropped from certain point crosses the top and bottom ends of a vertical pole of length 20m in one second the distance of top of the pole from the initial point of release will be (g=10) Ans:11.25m

  1. physics

    A ball is dropped from an upper floor, some unknown distance above your apartment. As you look out of your window, which is 1.5 m tall, you observe that it takes the ball 0.18 seconds to traverse the length of the window.

  2. Algebra

    Scott set up a volleyball net in his backyard. one of the poles, which forms a right angle with the ground, is 6 feet high. To secure the pole, he attached a rope from the top of the pole to a stake 8 feet from the bottom of the

  3. Math

    A street light is at the top of a 16 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 8 ft/sec along a straight path. How fast is the tip of her shadow moving along the ground when she is 30 ft from the

  4. Calculus

    A street light is mounted at the top of a 6 meter tall pole. A man 2m tall walks away from the top with a speed of 1.5 m/s along a straight path. How fast is the tip of his shadow moving when he is 10m from the pole?

You can view more similar questions or ask a new question.