Answer:
a) d'(t) = 32t
The units of d'(t) are ft/s and it gives how fast or how slow the object is falling.
b) The ledge is 784 ft high
And just when the stone strikes the ground, it's moving at a speed of 152.73 miles/hour
Step-by-step explanation:
d(t) = 16t²
a) d'(t) = (d/dt)(d) = (d/dt) (16t²) = 32t
Since it is a time derivative, the units are ft/s and it describes the rate of change of the distance of falling object; more plainly, it gives how fast or how slow the object is falling.
b) d(t) = 16t²
If t = 7 s, how high is the ledge?
d(7) = 16 (7²) = 784 ft
How fast is the stone moving when it strikes the ground (in miles per hour)?
d'(t) = 32t
d'(7) = 32 × 7 = 224 ft/s
In miles/hour
224 ft/s = 224 ft/s × (1 mile/5280 ft) × (3600s/1 hr) = 152.73 miles/hour
