Answer:
V₀y = 0 m/s
t = 2.47 s
V₀ₓ = 61.86 m/s
Vₓ = 61.86 m/s
Explanation:
Since, the ball is hit horizontally, there is no vertical component of velocity at initial point. So, the initial vertical velocity (V₀y) will beL
<u>V₀y = 0 m/s</u>
For the initial vertical velocity of golf ball we consider the vertical motion and apply 2nd equation of motion:
Y = V₀y*t + (0.5)gt²
where,
Y = Height = 30 m
g = 9.8 m/s²
t = time to hit the ground = ?
Therefore,
30 m = (0 m/s)(t) + (0.5)(9.8 m/s²)t²
t² = 30 m/4.9 m/s²
t = √6.122 s²
<u>t = 2.47 s</u>
For initial vertical velocity we analyze the horizontal motion of the ball. We neglect the frictional effects in horizontal motion thus the speed remains uniform. Hence,
V₀ₓ = Xt
where,
V₀ₓ = Initial vertical Velocity = ?
X = Horizontal Distance = 25 m
Therefore,
V₀ₓ = (25 m)(2.47 s)
<u>V₀ₓ = 61.86 m/s</u>
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Due, to uniform motion in horizontal direction:
Final Vertical Velocity = Vₓ = V₀ₓ
Vₓ = 61.86 m/s
Answer:
Explanation:
The balance condition, to keep the gate from moving, requires that the net torque be zero, this is, the torques on both sides of the gate must be equal.
- Torque equation: τ = F × d
a) <u>Torque applied by one of the children:</u>
b) <u>Torque applied by the second child</u>:
c) <u>Equilibrium condition</u>:
- τ₁ = τ₂
- 170 N × 0.590m = F × 0.430m
- F = 170 N × 0.590 m / 0.430 m = 233 N ← answer
Answer:
The speed of the truck must be 9.8 ft/s.
The speed of the truck must be 17 ft/s
Explanation:
First, let´s calculate the distance of the car relative to the intersection at time t = 2 s and t = 6 s:
d(t) = 1.1 t² + t +2
d(2) = 1.1 (2)² + 2 + 2 = 8.40 ft
d(6) = 1.1(6)² + 6 + 2 = 47. 6 ft
The car traveled (47.6 ft - 8.40 ft) 39.2 ft in 4 seconds.
Then, the speed of the truck must be (39.2 ft / 4 s) 9.8 ft/s to cover the same distance as the car in 4 seconds.
Now, let´s find the distance of the car to the intersection at time t = 7 and t = 7.1.
d(7) = 1.1(7)² + 7 + 2 = 62.9 ft
d(7.1) = 1.1(7.1)² + 7.1 + 2 = 64.6 ft
The distance traveled by the car in 0.1 s is ( 64.6 ft - 62.9 ft) 1.7 ft
Then the truck must travel with a velocity of (1.7 ft /0.1s) 17 ft/s to cover that distance in 0.1 s.
Answer:
100N
Explanation:
Force = Mass x Acceleration
Force = 0.4 kg x 250 m/s2
Force = 100N