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183_notes:examples:finding_the_range_of_projectile [2014/07/22 06:27] – pwirving | 183_notes:examples:finding_the_range_of_projectile [2014/07/23 05:36] – pwirving | ||
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Diagram of forces acting on bus once it leaves the road. | Diagram of forces acting on bus once it leaves the road. | ||
- | {{183_notes: | + | {{183_notes: |
The general equation for calculating the final position of an object: | The general equation for calculating the final position of an object: | ||
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We now to find the range in the x and z directions in order to have a position vector for the final resting place of the bus. | We now to find the range in the x and z directions in order to have a position vector for the final resting place of the bus. | ||
+ | |||
+ | There is no force acting in the x or z directions as the only force acting on the system is the gravitational force which acts in the y-direction. | ||
+ | |||
+ | This means that the initial velocities in both of these directions have remained unchanged. | ||
+ | |||
+ | We know the amount of time the bus has been traveling in the x-direction at its initial velocity and its initial position so we can compute the distance travelled in this direction using the position update formula for x-components. | ||
$$ x_f = x_i + V_{avg,x} \Delta{t}$$ | $$ x_f = x_i + V_{avg,x} \Delta{t}$$ | ||
+ | |||
+ | Plug in respective values for variables. | ||
$$ = 0 + 80m/ | $$ = 0 + 80m/ | ||
+ | |||
+ | Compute range in x-direction. | ||
$$ = 767m$$ | $$ = 767m$$ | ||
+ | |||
+ | Repeat same process for the z-components: | ||
| | ||
$$ z_f = z_i + V_{avg,z} \Delta{t}$$ | $$ z_f = z_i + V_{avg,z} \Delta{t}$$ | ||
+ | |||
+ | Plug in respective values for variables. | ||
| | ||
$$ = -5 + -5m/ | $$ = -5 + -5m/ | ||
+ | |||
+ | Compute range in z-direction. | ||
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- | $$ = -52.95$$ | + | $$ = -52.95$$ |
+ | |||
+ | Write range(final position vector) using all components: | ||
- | Final position = $\langle 767, | + | Final position = $$\langle 767, |