Answer:
pf = 198.8 kg*m/s
θ = 46.8º N of E.
Explanation:
- Since total momentum is conserved, and momentum is a vector, the components of the momentum along two axes perpendicular each other must be conserved too.
- If we call the positive x- axis to the W-E direction, and the positive y-axis to the S-N direction, we can write the following equation for the initial momentum along the x-axis:
- We can do exactly the same for the initial momentum along the y-axis:
- The final momentum along the x-axis, since the collision is inelastic and both objects stick together after the collision, can be written as follows:
- We can repeat the process for the y-axis, as follows:
- Since (1) is equal to (3), replacing for the givens, and since p₀Bₓ = 0, we can solve for vfₓ as follows:
- In the same way, we can find the component of the final momentum along the y-axis, as follows:
- With the values of vfx and vfy, we can find the magnitude of the final speed of the two-object system, applying the Pythagorean Theorem, as follows:
- The magnitude of the final total momentum is just the product of the combined mass of both objects times the magnitude of the final speed:
- Finally, the angle that the final momentum vector makes with the positive x-axis, is the same that the final velocity vector makes with it.
- We can find this angle applying the definition of tangent of an angle, as follows:
⇒ θ = tg⁻¹ (1.06) = 46.8º N of E
Answer:
e = 0.0898m
v = 2.07m/s
Explanation:
a) According to Hooke's law
F = ke
e is the extension
k is the spring constant
Since F = mg
mg = ke
e = mg/k
Substitute the given value
e = 1.1(9.8)/120
e = 10.78/120
e = 0.0898m
Hence it is stretched by 0.0898m from its unstrained length
2) Total Energy = PE+KE+Elastic potential
Total Energy = mgh +1/2mv²+1/2ke²
Substitute the given value
5.0= 1.1(9.8)(0.2)+1/2(1.1)v²+1/2(120)(0.0898)²
Solve for v
5.0 = 2.156+0.55v²+0.48338
5.0-2.156-0.48338= 0.55v²
2.36 =0.55v²
v² = 2.36/0.55
v² = 4.29
v ,= √4.29
v = 2.07m/s
Hence the required velocity is 9.28m/s
Answer:
Let's say the pitcher is angry or just has a really heavy hand while throwing this ball, and now you have to catch it, otherwise it's going to ram into your face. When you put your hands up just in time to catch this ball, this is called impulse, or commonly expressed as a reflex. Depending on what kind of ball is being thrown, such as a golf ball, baseball, basketball, beach-ball, rubber-ball, baseball, etc. ... the weight of the ball itself is going to impact how much it i going to hurt when you catch it without any hand protection. However, if you're catching, let's say a baseball, with a padded glove, it is not going to hurt as bad as catching the baseball bare handed, because the padded glove has enough padding in it to create a barrier between the skin of your hand and the palm of the glove.
Answer:
13.18 m/s
Explanation:
Let the velocity of sports utility car is
-u as it is moving in opposite direction.
mc = 1200 kg, uc = 31.1 m/s
ms = 2830 kg, us = - u = ?
Using conservation of momentum
mc × uc + ms × us = 0
1200 × 31.1 - 2830 × u = 0
u = 13.18 m/s
Angular acceleration is simply the ratio of the Torque
over the rotation inertia, that is:
Angular acceleration = Torque / Rotational inertia
So substituting the values:
Angular acceleration = 2.4 N m / 4.0 kg m2
<span>Angular acceleration = 0.7 rad/s^2</span>
