Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

A lamp is 50 feet above the ground . A ball is dropped from the same height at a point which is at a distance of 30 feet away from the light pole. If ball falls a distance s=16t 2 feet in t seconds . Then how fast is the shadow of the ball moving along the ground ½ s later?

A lamp is 50 feet above the ground . A ball is dropped from the same height at a point which is at a distance of 30 feet away from the light pole. If ball falls a distance  s=16t2 feet in t seconds . Then how fast is the shadow of the ball moving along the ground ½ s later?

Grade:12

1 Answers

Arun
25763 Points
4 years ago
Dear Raghav
 
Draw a figure to represent the situation when the ball has fallen a distance s feet from its initial position. Let x = distance along the ground from the point immediately below the ball to the point where the shadow of the ball meets the ground. We then have two similar triangles and can write down the ratio of corresponding sides in the form: x 30 ------- = ------- 50-s sWe also have ds/dt = 32t and we are required to find dx/dt when t = 1/2Multiplying out we get xs = 1500 - 30s and differentiating x(ds/dt) + s(dx/dt) = -30(ds/dt)at t=1/2 ds/dt = 16 s = 16(1/4) = 4 and 4x = 1500 - 120 x = 345 ft So 345(16) + 4(dx/dt) = -30(16) 4(dx/dt) = -6000 dx/dt = -1500 ft/secSo at this moment the shadow is moving at a speed 1500 ft/sec towards the point immediately below the ball. The high speed is to be expected since initially the shadow is at infinity and has to move to the end point in 1.76 seconds.
 
Regards
Arun (askIITians forum expert)

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free