To solve this problem it is necessary to apply the concepts related to Newton's second law and the kinematic equations of movement description.
Newton's second law is defined as
Where,
m = mass
a = acceleration
From this equation we can figure the acceleration out, then
From the cinematic equations of motion we know that
Where,
Final velocity
Initial velocity
a = acceleration
x = displacement
There is not Final velocity and the acceleration is equal to the gravity, then
From the equation of motion where acceleration is equal to the velocity in function of time we have
Therefore the time required is 0.0705s
Answer:
= 3289.8 m / s
Explanation:
This exercise can be solved using the definition of momentum
I = ∫ F dt
Let's replace and calculate
I = ∫ (at - bt²) dt
We integrate
I = a t² / 2 - b t³ / 3
We evaluate between the lower limits I=0 for t = 0 s and higher I=I for t = 2.74 ms
I = a (2,74² / 2- 0) - b (2,74³ / 3 -0)
I = a 3,754 - b 6,857
We substitute the values of a and b
I = 1500 3,754 - 20 6,857
I = 5,631 - 137.14
I = 5493.9 N s
Now let's use the relationship between momentum and momentum
I = Δp = m - m v₀o
I = m - 0
= I / m
= 5493.9 /1.67
= 3289.8 m / s
Answer:
your friend will wait for you for 2.2 minutes.
Explanation:
Given;
Distance of the journey, d = 50 km
your speed, v₁ = 88.5 km/h
your friends speed, v₂ = 94.5 km/h
The time taken before you reached the end of the trip;
The time taken before your friend reached the end of the trip;
The difference in time = (0.565 - 0.529) hour
= 0.036 hour
= 0.036 x 60 min
= 2.2 mins
Therefore, your friend will wait for you for 2.2 minutes.
Answer:
The height from which the ball was thrown is 18.82 m
Explanation:
Given;
horizontal velocity of the ball, vi = 27.0 m/s
horizontal distance of the ball, d = 53.0 m
Apply kinematic equation, to determine the time taken for the ball to make a horizontal distance of 53.0 m.
d = vt
t = d/v
t = 53/27
t = 1.96 seconds
This time is equal to the time the ball spent in air before hitting the ground.
The vertical distance at this time, is the height from which the ball was thrown, and it is calculated as;
h = vt + ¹/₂gt²
v is vertical velocity, = 0
g is acceleration due to gravity
h = ¹/₂ x 9.8 x (1.96)²
h = 18.82 m
Therefore, the height from which the ball was thrown is 18.82 m
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