Answer: 211.059 m
Explanation:
We have the following data:
The angle at which the ball leaves the bat
The initial velocity of the ball
The acceleration due gravity
We need to find how far (horizontally) the ball travels in the air: 
Firstly we need to know this velocity has two components:
<u>Horizontally:</u>
(1)
(2)
<u>Vertically:</u>
(3)
(4)
On the other hand, when we talk about parabolic movement (as in this situation) the ball reaches its maximum height just in the middle of this parabola, when
and the time
is half the time it takes the complete parabolic path.
So, if we use the following equation, we will find
:
(5)
Isolating
:
(6)
(7)
(8)
Now that we have the time it takes to the ball to travel half of is path, we can find the total time
it takes the complete parabolic path, which is twice
:
(9)
With this result in mind, we can finally calculate how far the ball travels in the air:
(10)
Substituting (2) and (9) in (10):
(11)
Finally:
Time=speed/acceleration
Gravitaional Acceleration=9.8 m/s^2
Speed=24.5 m/s
Time=24.5/9.8=2.5 s
Answer:
F_Balance = 46.6 N ,m' = 4,755 kg
Explanation:
In this exercise, when the sphere is placed on the balance, it indicates the weight of the sphere, when another sphere of opposite charge is placed, they are attracted so that the balance reading decreases, resulting in
∑ F = 0
Fe –W + F_Balance = 0
F_Balance = - Fe + W
The electric force is given by Coulomb's law
Fe = k q₁ q₂ / r₂
The weight is
W = mg
Let's replace
F_Balance = mg - k q₁q₂ / r₂
Let's reduce the magnitudes to the SI system
q₁ = + 8 μC = +8 10⁻⁶ C
q₂ = - 3 μC = - 3 10⁻⁶ C
r = 0.3 m = 0.3 m
Let's calculate
F_Balance = 5 9.8 - 8.99 10⁹ 8 10⁻⁶ 3 10⁻⁶ / (0.3)²
F_Balance = 49 - 2,397
F_Balance = 46.6 N
This is the balance reading, if it is calibrated in kg, it must be divided by the value of the gravity acceleration.
Mass reading is
m' = F_Balance / g
m' = 46.6 /9.8
m' = 4,755 kg
Answer:
21870.3156 N
Explanation:
u = Initial velocity
v = Final velocity
s = Displacement
a = Acceleration
g = Acceleration due to gravity = 1.6 m/s²
Equation of motion

The acceleration of the craft should be 1.02234 m/s²

Weight of the craft

Thrust

The thrust needed to reduce the velocity to zero at the instant when the craft touches the lunar surface is 21870.3156 N