King Arthur's knights use a catapult to launch a rock from their vantage point on top of the castle wall, 14 m above the moat. The rock is launched at a speed of 27 m/s and an angle of 32degrees above the horizontal.
Finding out the acceleration 12/3 = 4m/s^2
thus it is descending so the actual acceleration would be 9.8-4 = 5.8 m/s^2
the weight will be 90*5.8 = 522 N
522/9.8 = 53.2 kg
Answer:
13 m/s east
Explanation:
We can solve the problem by using the law of conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision:

where
m = 0.1 kg is the mass of each puck
u1 = +13 m/s is the initial velocity of puck 1
u2 = -18 m/s is the initial velocity of puck 2 (here I assume the west direction to be the negative direction, so I put a negative sign)
v1 = -18 m/s is the final velocity of puck 1
v2 = ? is the final velocity of puck 2
Simplifying m from the formula and substituting the data, we can find the final velocity of puck 2, v2:

And the positive sign means that puck 2 is moving east.
Answer: 1.9 m/s
Explanation:
1) Data:
height, y = 0
range, x = 0.77m
angle, α = 45°
question, horizontal velocity, Vox = ?
2) Physical principles and formulas
Projectile motion.

3) Solution


Factor
![0=t[V_0sin(45)-gt/2]](https://tex.z-dn.net/?f=%200%3Dt%5BV_0sin%2845%29-gt%2F2%5D%20)
Discard t = 0 and solve for the other factor:
![gt/2=V_0sin(45)\\ \\ V_0= gt/(2sin(45))=9.81[0.77/V_{0}cos(45)]/[2sin(45)]\\ \\ V_0^2=9.81[0.77/(2cos(45)sin(45)=9.81[0.77/sin(90)]=7.55\\ \\ V_0}=\sqrt{7.55} =2.8](https://tex.z-dn.net/?f=%20gt%2F2%3DV_0sin%2845%29%5C%5C%20%5C%5C%20%20V_0%3D%20gt%2F%282sin%2845%29%29%3D9.81%5B0.77%2FV_%7B0%7Dcos%2845%29%5D%2F%5B2sin%2845%29%5D%5C%5C%20%5C%5C%20V_0%5E2%3D9.81%5B0.77%2F%282cos%2845%29sin%2845%29%3D9.81%5B0.77%2Fsin%2890%29%5D%3D7.55%5C%5C%20%5C%5C%20V_0%7D%3D%5Csqrt%7B7.55%7D%20%3D2.8%20%20)
Find Vx:
![Vx=V_{0x}=V_{0}cos(45)=2.75(\sqrt{2} /2]=1.9](https://tex.z-dn.net/?f=%20Vx%3DV_%7B0x%7D%3DV_%7B0%7Dcos%2845%29%3D2.75%28%5Csqrt%7B2%7D%20%2F2%5D%3D1.9%20%20)
Vx = 1.9m/s ← answer
Answer:
300 N
Explanation:
force = mass × acceleration
= 60 kg × 5m/s^2
= 300 N