The deck of a bridge is suspended 275 feet above a river. If a pebble falls off the side of the bridge, the height, in feet, of the pebble above the water surface after t seconds is given by y − 275 2 16t 2. (a) Find the average velocity of the pebble for the time period beginning when t − 4 and lasting (i) 0.1 seconds (ii) 0.05 seconds (iii) 0.01 seconds (b) Estimate the instantaneous velocity of the pebble after 4 seconds.

1. Average velocity

When t=4

i. [4, 4.1]

= y(4.1) - y(4) / 4.1 - 4

= 275 - 16(4.1)^2 - 275 - 16(4)^2 / 0.1

= 275 - 16*16.81 - 275 - 16(16) / 0.1

= 6.04 - 19 / 0.1

= -12.96 /0.1

= -129.6

ii. [4, 4.05]

= y(4.05) - y(4) / 4.05 - 4

= 275 - 16(4.05)^2 - 275 - 16(4)^2 / 0.05

= 275 - 16*16.40 - 275 - 16(16) / 0.05

= 12.6 - 19 / 0.05

= -6.4 / 0.05

= -128

iii. [4, 4.01]

= y(4.01) - y(4) / 4.01 - 4

= 275 - 16(4.01)^2 - 275 - 16(4)^2 / 0.01

= 275 - 16*16.08 - 275 - 16(16) / 0.01

= 17.72 - 19 / 0.01

= -1.28 / 0.01

= -128

b. Instantaneous velocity

y = 275 - 16t^2

dy/dx = -32t

Considering t = 4

Instantaneous velocity after 4 seconds = -32(4)

Instantaneous velocity after 4 seconds = -128