Answer:
Explanation:
We will use the KE equation you wrote here and fill in what we are given:
and isolating the m:
which gives us
m = .50 kg
Answer:
2 secs; 65 feet
Explanation:
The function guiding the water bottle is given as:
f(x) = -16t² + 64t + 1
The bottle will reach maximum height when velocity, df/dt (velocity is the first derivative of distance) = 0.
Therefore:
df/dt = 0 = -32t + 64
=> 32t = 64
t = 64/32 = 2 seconds
This is the time it will take to reach the maximum height.
To find this height, we insert t = 2 into the function f(x):
f = -16(2)² + 64(2) + 1
f = -(16 * 4) + 128 + 1
f = -64 + 128 + 1
f = 65 ft
Its maximum height is 65 ft.
This question is solved using an available similar problem as data provided for the forces was not given.
Repeat the same steps outlined for your problem.
Regards.
Answer:
F = 1.598 KN , Q = 90 degree (+ y-axis)
Explanation:
Sum of Forces in x-direction to the left (+)
2 cos (30) + 3cos (60) + F*cos (Q) = F_a ..... 1
Sum of Forces in y-direction to the up (+)
2 sin (30) + F*sin (Q) - 3 sin (60) ...... 2
Using Eq 2 and solve:
F*sin (Q) = 1.598 KN
F_min when sin (Q) is max, max possible value of sin(Q) = 1 @ Q = 90 degrees.
Hence,
F_min = 1.598 KN
Using Eq 1 @ Q = 90 degrees and F = 1.598 KN:
F_a = 2 cos (30) + 3cos (60) = 3.2 KN
Answer:
34.3 m/s
Explanation:
Newton's Second Law states that the resultant of the forces acting on the car is equal to the product between the mass of the car, m, and the centripetal acceleration
(because the car is moving of circular motion). So at the top of the hill the equation of the forces is:

where
(mg) is the weight of the car (downward), with m being the car's mass and g=9.8 m/s^2 is the acceleration due to gravity
R is the normal reaction exerted by the road on the car (upward, so with negative sign)
v is the speed of the car
r = 0.120 km = 120 m is the radius of the curve
The problem is asking for the speed that the car would have when it tires just barely lose contact with the road: this means requiring that the normal reaction is zero, R=0. Substituting into the equation and solving for v, we find:

Answer:(a) 50 N
(b)38.34 N
Explanation:
Given
Maximum tension(T) in line 50 N
(a)If line is moving up with constant velocity i.e. there is no acceleration
This will happen when Tension is equal to weight of Fish
T-mg=0
T=mg
Maximum weight in this case will be 50 N
(b)acceleration of magnitude 
T-mg=ma


m=3.91
Therefore weight is 