We know, by conservation of energy :
Therefore,
Putting given values, we get :
Therefore, the spring be compressed to 6.93 cm to send the ball twice as high.
Hence, this is the required solution.
(a) Fx = 1.464 N
(b) Fy = 1.952 N
(c) F(x, y) = 1.464 i + 1.952 j
Given
Mass = 1kg
Acceleration = 2.44 m/s2
Angle with positive X axis = 53°
As we know
F = ma
By substituting value
F= 1×2.44 N
F= 2.44 N
(a) Component of force in X direction
Fx = F Cosθ
Fx = 2.44 Cos(53°)
Fx = 2.44 × 0.60 = 1.464 N
(b) Component of force in Y direction
Fy = F Sinθ
Fy = 2.44 Sin(53°) = 2.44 × 0.80 = 1.952 N
(c) Net force in vector notation
F(x, y) = 1.464 i + 1.952 j
Thus we got net force.
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Answer: Remember speed is distance divided by time, so if he travels 1000 m in 7.045 s, his speed is
(1000 m)/(7.045 s) = 141.9 m/s.
Note there are 1609 metres in a mile, or 1 mi = 1609 m, so m = 1/1609 mi, or
141.9/1609 mi/s = 0.08822 mi/s. Now, note that 1 h = 3600 s, so the speed is
0.08822*3600 mi/h = 317.6 mi/h.
More mass and less difference
Combine all of the x's on one side of the equation and then finish the problem!
