Answer:
Lauch velocity (u) = 26.15 m/s
Lauch Angle (θ) = 35°
Explanation:
From the question given above, the following data were obtained:
Range (R) = 65 m
Time of flight (T) = 3 s
Acceleration due to gravity (g) = 10 m/s²
Lauch velocity (u) =?
Lauch Angle (θ) =?
R = u²Sin2θ /g
65 = u² × Sin2θ /10
Recall:
Sin2θ = 2SinθCosθ
65 = u² × 2SinθCosθ / 10
65 = u² × SinθCosθ / 5
Cross multiply
65 × 5 = u² × SinθCosθ
325 = u² × SinθCosθ .....(1)
T = 2uSinθ / g
3 = 2uSinθ / 10
3 = uSinθ / 5
Cross multiply
3 × 5 = uSinθ
15 = u × Sinθ
Divide both side by Sinθ
u = 15 / Sinθ....... (2)
Substitute the value of u in equation (2) into equation (1)
325 = u² × SinθCosθ
u = 15 / Sinθ
325 = (15 / Sinθ)² × SinθCosθ
325 = 225 / Sin²θ × SinθCosθ
325 = 225 × SinθCosθ / Sin²θ
325 = 225 × Cosθ / Sinθ
Cross multiply
325 × Sineθ = 225 × Cosθ
Divide both side by Cosθ
325 × Sineθ / Cosθ = 225
Divide both side by 325
Sineθ / Cosθ = 225 / 325
Sineθ / Cosθ = 0.6923
Recall:
Sineθ / Cosθ = Tanθ
Tanθ = 0.6923
Take the inverse of Tan
θ = Tan¯¹ 0.6923
θ = 35°
Substitute the value of θ into equation (2) to obtain the value of u.
u = 15 / Sinθ
θ = 35°
u = 15 / Sin 35
u = 15 / 0.5736
u = 26.15 m/s
Summary:
Lauch velocity (u) = 26.15 m/s
Lauch Angle (θ) = 35°
Explanation:
Distance d=1.5×108 km=1.5×1011 m
Mass of the sun, m=2×1030 kg
Mass of the earth, M=6×1024 kg
Force of gravitation, F=G×d2m×M
F=6.7×10−11×(1.5×1011)22×1030×6×1024=3.57×1022 N
First picture (black background): 50 Newtons UP
Second picture (white background): 30 Newtons RIGHT
Answer:
12900 W
24200 W
Explanation:
Given:
v₀ = 0 m/s
v = 1.3 m/s
t = 2.0 s
Find: a and Δx
v = at + v₀
(1.3 m/s) = a (2.0 s) + (0 m/s)
a = 0.65 m/s²
Δx = ½ (v + v₀) t
Δx = ½ (1.3 m/s + 0 m/s) (2.0 s)
Δx = 1.3 m
While accelerating:
Newton's second law:
∑F = ma
F − mg = ma
F = m (g + a)
F = (1500 kg + 400 kg) (9.8 m/s² + 0.65 m/s²)
F = 19855 N
Power = work / time
P = W / t
P = Fd / t
P = (19855 N) (1.3 m) / (2.0 s)
P ≈ 12900 W
At constant speed:
Newton's second law:
∑F = ma
F − mg = 0
F = mg
F = (1500 kg + 400 kg) (9.8 m/s²)
F = 18620 N
Power = work / time
P = W / t
P = Fd / t
P = Fv
P = (18620 N) (1.3 m/s)
P ≈ 24200 W
<span>This problem is solved by the equation of motion:
x = x0 + v0*t + 1/2*a*t^2,
Here x0 = 0, v0 = 40ft/sec and a = -5 ft/s^2, we need to solve for t:
v = v0 + a*t, solve how long does it take to stop: 0 = v0 + a*t --> a*t = -v0 --> t = -v0/a
-- > 40/5 = 8 seconds to stop.
In this time, the car travels x = 0 + 40*8 + 0.5*-5*8^2 ft ~ 160 ft.
Answer: The car travels 160 ft.</span>
