Given Information:
Initial speed of rock = vi = 30 m/s
escape speed of the asteroid = ve = 24 m/s
Required Information:
final speed of rock = vf = ?
Answer:
vf = 18 m/s
Explanation:
As we know from the conservation of energy
KEf + Uf = KEi + Ui
Where KE is the kinetic energy and U is the potential energy
0 + 0 = ½mve² - GMm/R
When escape speed is used, KEf is zero due to vf being zero. Uf is zero because the object is very far away from mass M, therefore, the equation becomes
GMm/R = ½mve²
m cancels out
GM/R = ½ve²
GM/R = ½(24)²
GM/R = 288
KEf + Uf = KEi + Ui
½mvi² + 0 = ½vf² - GMm/R
m cancels out
½vi² = ½vf² - GM/R
Substitute the values
½(30)² = ½vf² - (288)
½vf² = 450 - 288
vf² = 2(162)
vf = √324
vf = 18 m/s
Therefore, the final speed of the rock is 18 m/s
Answer:
3) D: 31 m/s
4) D: 84.84 metres
Explanation:
3) Initial velocity along the x-axis is;
v_x = v_o•cos θ
Initial velocity along the y-axis is;
v_y = v_o•sin θ
Plugging in the relevant values, we have;
v_x = 31 cos 60
v_x = 31 × 0.5
v_x = 15.5 m/s
Similarly,
v_y = 31 sin 60
v_y = 31 × 0.8660
v_y = 26.85 m/s
Thus, magnitude of the initial velocity is;
v = √(15.5² + 26.85²)
v ≈ 31 m/s
4) Formula for horizontal range is;
R = (v² sin 2θ)/g
R = (31² × sin (2 × 60))/9.81
R = 84.84 m
We know, Volume = Mass / Density
Here, mass = 4 Kg = 4000 g
d = 1,897 g/ml
Substitute their values,
v = 4000 / 1897
v = 2.108 ml
In short, Your Answer would be 2.108 mL
Hope this helps!
Answer:
(A) it's acceleration is negative but but it's velocity is positive
Explanation:
In the question it is given that begins to slow down so its speed is decreasing it is does not means that its speed is negative
For example let first the velocity of the car is 30 m/sec and when its velocity decreases it becomes 20 m/sec in 5 sec
So it is not negative at all
Now the acceleration is the rate of change of velocity


So acceleration is negative here
So option (a) will be the correct option