Answer:
144 ft
Explanation:
h(t) = -16t² + 64t + 80
The maximum height is at the vertex. We can find the vertex of a parabola using -b / (2a):
t = -64 / (2×-16)
t = 2
The vertex is at 2 seconds. The height of the stone at this time is:
h(2) = -16(2)² + 64(2) + 80
h(2) = 144
The maximum height is 144 feet.
Answer:
(a) The magnitude of the applied force is (0.0001524k) Newton
(b) Corresponding stress in the steel core = (0.0001524k/area) Newton per meter square
Explanation:
(a) From Hookes law of elasticity,
Force applied = force constant (k) × compression
compression = 0.006 in = 0.006 × 0.0254 = 0.0001524 meter
Force applied = k × 0.0001524 = (0.0001524k) Newton
(b) Stress = Force applied (Newton)/area of steel core (meter square) = (0.0001524k/area) Newton per meter square
Explanation:
The runner was 8.6km away from the finish line when the bird starts flying.
Therefore it takes the bird 8.6/14.4 = 0.60 hours for the bird to fly to the finish line.
In that 0.60 hours, the runner would have ran an extra 3.6km/h * 0.6h = 2.16km.
Now, the runner and the bird are flying towards each other. The distance between them is 8.6 - 2.16 = 6.44km and their combined speed is 18.0km.
Hence, they will meet in 6.44/18.0 = 0.36 hours.
Overall, the bird flew for 0.60 + 0.36 = 0.96 hours, and flew 14.4km/h * 0.96h = 13.8km.