Answer:
(a) The angle of projection is 63 degree.
(b) The velocity of projection is 24.5 m/s.
Explanation:
Height, h = 1 m
horizontal distance, d = 50 m
time, t = 4.5 s
Let the initial velocity is u and the angle is A.
(a) Horizontal distance = horizontal velocity x time
50 = u cos A x 4.5
u cos A = 11.1 .....(1)
Use second equation of motion in vertical direction
Divide (2) by (1)
tan A = 1.97
A = 63 degree
(b) Substitute the value of A in equation (2)
u x sin 63 = 21.8
u = 24.5 m/s
<span>A gymnast with mass m1 = 43 kg is on a balance beam that sits on (but is not attached to) two supports. The beam has a mass m2 = 115 kg and length L = 5 m. Each support is 1/3 of the way from each end. Initially the gymnast stands at the left end of the beam.
1)What is the force the left support exerts on the beam?
2)What is the force the right support exerts on the beam?
3)How much extra mass could the gymnast hold before the beam begins to tip?
Now the gymnast (not holding any additional mass) walks directly above the right support.
4)What is the force the left support exerts on the beam?
5)What is the force the right support exerts on the beam?</span>
Answer:
(a)
(b)
Explanation:
Represent losing with L and winning with W.
So:
--- Given
Probability of winning would be:
The question illustrates binomial probability and will be solved using the following binomial expansion;
So:
Solving (a): Winning at least 1
We look at the above and we list out the terms where the powers of W is at least 1; i.e., 1,2,3 and 4
So, we have:
Substitute value for W and L
<em>Hence, the probability of her winning at least one is 0.7599</em>
Solving (a): Wining exactly 2
We look at the above and we list out the terms where the powers of W is exactly 2
So, we have:
Substitute value for W and L
<em>Hence, the probability of her winning exactly two is 0.2646</em>
Answer:
velocity = 62.89 m/s in 58 degree measured from the x-axis
Explanation:
Relevant information:
Before the collision, asteroid A of mass 1,000 kg moved at 100 m/s, and asteroid B of mass 2,000 kg moved at 80 m/s.
Two asteroids moving with velocities collide at right angles and stick together. Asteroid A initially moving to right direction and asteroid B initially move in the upward direction.
Before collision Momentum of A = 1000 x 100 = kg - m/s in the right direction.
Before collision Momentum of B = 2000 x 80 = 1.6 x kg - m/s in upward direction.
Mass of System of after collision = 1000 + 2000 = 3000 kg
Now applying the Momentum Conservation, we get
Initial momentum in right direction = final momentum in right direction =
And, Initial momentum in upward direction = Final momentum in upward direction = 1.6 x
So, = m/s
and m/s
Therefore, velocity is =
=
= 62.89 m/s
And direction is
tan θ = = 1.6
therefore,
= from x-axis