Answer:
x = A sin ω t describes the displacement of the particle
v = A ω cos ω t
a = -A ω^2 sin ω t
a (max) = -A ω^2 is the max acceleration (- can be ignored here)
ω = (K/ m)^1/2 for SHM
F = - K x^2 restoring force of spring
K = 4.34 / .0745^2 = 782 N / m
ω = (782 / .297)^1/2 = 51.3 / sec
a (max) = .0745 * 782 / .297 = 196 m / s^2
Answer:
8) 1500 feet
9) 20 miles
10) 4 Days
11) 2250 miles
12) 1 hour and 5 minutes
13) 27.27miles per hour
Explanation
8) There are 60 seconds in one minute so 60x25=1500 feet
9) 30 minutes is half of an hour so 40 miles ÷ 2 = 20 miles
10) 12x4=48
11) 500 miles x 4.5 hours is 2250 miles
12) Train leaves at 3pm after 60 miles it will be 4 pm and after 5 more miles 4:05 pm so 1 hour and 5 minutes
13)
Elmo = 40 minutes and 5 miles
Bert and Ernie = 45 minutes and 15 miles
Cookie Monster = 20 minutes and 10 miles
Home = 5 minutes abd 20 miles
Average Speed including stops is 27.27 miles per hour
1750 meters.
First, determine how long it takes for the kit to hit the ground. Distance over constant acceleration is:
d = 1/2 A T^2
where
d = distance
A = acceleration
T = time
Solving for T, gives
d = 1/2 A T^2
2d = A T^2
2d/A = T^2
sqrt(2d/A) = T
Substitute the known values and calculate.
sqrt(2d/A) = T
sqrt(2* 1500m / 9.8 m/s^2) = T
sqrt(3000m / 9.8 m/s^2) = T
sqrt(306.122449 s^2) = T
17.49635531 s = T
Rounding to 4 significant figures gives 17.50 seconds. Since it will take
17.50 seconds for the kit to hit the ground, the kit needs to be dropped 17.50
seconds before the plane goes overhead. So just simply multiply by the velocity.
17.50 s * 100 m/s = 1750 m
