A certain sports car can accelerate from 0 m/s to 27.7 m/sec with an acceleration of 11.2 m/s². How long does this acceleration
1 answer:
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Answer:
a) x = v₀² sin 2θ / g
b) t_total = 2 v₀ sin θ / g
c) x = 16.7 m
Explanation:
This is a projectile launching exercise, let's use trigonometry to find the components of the initial velocity
sin θ = / vo
cos θ = v₀ₓ / vo
v_{oy} = v_{o} sin θ
v₀ₓ = v₀ cos θ
v_{oy} = 13.5 sin 32 = 7.15 m / s
v₀ₓ = 13.5 cos 32 = 11.45 m / s
a) In the x axis there is no acceleration so the velocity is constant
v₀ₓ = x / t
x = v₀ₓ t
the time the ball is in the air is twice the time to reach the maximum height, where the vertical speed is zero
v_{y} = v_{oy} - gt
0 = v₀ sin θ - gt
t = v_{o} sin θ / g
we substitute
x = v₀ cos θ (2 v_{o} sin θ / g)
x = v₀² /g 2 cos θ sin θ
x = v₀² sin 2θ / g
at the point where the receiver receives the ball is at the same height, so this coincides with the range of the projectile launch,
b) The acceleration to which the ball is subjected is equal in the rise and fall, therefore it takes the same time for both parties, let's find the rise time
at the highest point the vertical speed is zero
v_{y} = v_{oy} - gt
v_{y} = 0
t = v_{oy} / g
t = v₀ sin θ / g
as the time to get on and off is the same the total time or flight time is
t_total = 2 t
t_total = 2 v₀ sin θ / g
c) we calculate
x = 13.5 2 sin (2 32) / 9.8
x = 16.7 m
Answer:
Resultant force, R = 10 N
Explanation:
It is given that,
Force acting along +x direction,
Force acting along +y direction,
Both the forces are acting on a point object located at the origin. Let the resultant force of the object is given by R. So,
Here
R = 10 N
So, the resultant force on the object is 10 N. Hence, this is the required solution.
Answer:
<h2>4.6 m/s²</h2>Explanation:
The acceleration of an object given it's velocity and time taken can be found by using the formula
<h3>where
v is the final velocity
u is the initial velocity
t is the time taken
a is the acceleration
Since the body is from rest u = 0
From the question we have
We have the final answer as
<h3>4.6 m/s²</h3>Hope this helps you