math
posted by rolan .
A street light (light source) is 15 m above the ground. A ball is freely released from a location of 9 m from the light with the same elevation as the lightâ€™s. While the ball is falling, it casts a shadow on the ground. Assuming the gravity is 10 m/s2, calculate the speed of the shadow of the ball at 0.5 s after the ball has been released.

the height y of the ball at time t is
y = 15  5t^2
The shadow's position x meters from where the ball will hit, is found by using similar triangles:
y/x = 15/(9+x)
(15  5t^2)/x = 15/(9+x)
dx/dt = (9+x)/t
at t = .5, x = 99, so
dx/dt = (9+99)/(.5) = 216 m/s
Respond to this Question
Similar Questions

calc
A light is at the top of a pole 80ft high. A ball is dropped at the same height from a point 20ft from the light. If the ball falls according to 2=16t^2, how fast is the shadow of the ball moving along the ground 1 second later? 
Physics
When you approach a blinking source of light, the frequency of its blinking is seen to: decrease, increase, or remain the same always. I THINK IT IS INCREASING. If you are traveling at close to the speed of light and shine a flashlight … 
trig
Lindsay is out one night and notices that her body casts a shadow that is 1.8m long when she is standing 5mfrom the pole supporting a street light Lindsay is 1.5m tall. 1what is the angle of elevation to the street light ? 
trig
Lindsay is out one night and notices that her body casts a shadow that is 1.8m long when she is standing 5mfrom the pole supporting a street light Lindsay is 1.5m tall. 1what is the angle of elevation to the street light ? 
Physics
Subject: Light and Geometric Optics Question: Where must a light source be placed in front of a concave mirror for a) light energy to be concentrated to a single point b)the light to be reflected in a parallel beam? 
Geometry
A 195 cm person casts a 2.1 m shadow in the light of a street lamp. If the person is standing 4.2 m from the light, how tall is the light? 
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? 
Physics
Why is it necessary to collimate the light source before using the prism to disperse the light? 
math
a boy is walking at dusk and notices his shado from a nearby street light. the boy is 5 feet tall and the street light is 12 feet above the ground. When the boy is 4 feet from the base of the street light how long will his shadow be? 
math
A light is at the top of a pole 80 feet high. A ball is dropped at the same height from a point 20 feet away from the light. A wall 80 feet high, 60 feet away from the light is built. Assuming the ball falls according to the Newtonian …