Answer:
-1.5m/s²
Explanation:
Acceleration can be thought of as [Change in Velocity]/[Change in time]. To find these changes, you simply subtract the initial quantity from the final quantity.
So for this question you have:
- V_i = 110m/s
- V_f = 80m/s
- t_i = 0s
- t_f = 20s
which means that the acceleration = (80-110)/(20-0)[m/s²] = (-30/20)m/s² = -1.5m/s²
First, find the amount of time for the dart to hit the board using this equation: t = d/v
t = 2 m/ 15 m/s = 0.133 s
Then, find the height the dart has fallen from its initial point using this equation: h = 0.5gt²
h = 0.5(9.81 m/s²)(0.133 s)² = 0.0872 m or 8.72 cm
Since the diameter of the bull's eye is only 5 cm, and you started at the same level of the top of the bull's eye, that means the maximum allowance would only be 5 cm. Since it exceeded to 8.72 cm, it means that <em>Veronica will not hit the bull's eye.</em>
<span>When the fuel of the rocket is consumed, the acceleration would be zero. However, at this phase the rocket would still be going up until all the forces of gravity would dominate and change the direction of the rocket. We need to calculate two distances, one from the ground until the point where the fuel is consumed and from that point to the point where the gravity would change the direction.
Given:
a = 86 m/s^2
t = 1.7 s
Solution:
d = vi (t) + 0.5 (a) (t^2)
d = (0) (1.7) + 0.5 (86) (1.7)^2
d = 124.27 m
vf = vi + at
vf = 0 + 86 (1.7)
vf = 146.2 m/s (velocity when the fuel is consumed completely)
Then, we calculate the time it takes until it reaches the maximum height.
vf = vi + at
0 = 146.2 + (-9.8) (t)
t = 14.92 s
Then, the second distance
d= vi (t) + 0.5 (a) (t^2)
d = 146.2 (14.92) + 0.5 (-9.8) (14.92^2)
d = 1090.53 m
Then, we determine the maximum altitude:
d1 + d2 = 124.27 m + 1090.53 m = 1214.8 m</span>
Answer:
A larger force than 70 N will be required for the box to continue moving
Explanation:
A ramp is an inclined plane surface that is tilted to form a slope on its opposite sides
A ramp provides mechanical advantage or force amplification, by allowing less force to lift heavier load from having to move through a longer distance to reach a particular elevation when the slope of the ramp is gentle
Therefore, when the slope is steeper, and shorter, more force than 70 N will be required for the box to continue moving.
