1. A person runs 800. m at an average speed of 6.00 m/s and then the next 800. m at an average speed of 8.00 m/s. Calculate (a) the total time of travel and (b) the average speed.
2. A boy kicked a can horizontally from a 6.5 m high rock with a speed of 4.0 m/s. How far from the base of the rock the can land?
1. See previous post:Tue,6-17-14,9:52 PM
2. Xo = 4.0 m/s.
h = 0.5g*t^2 = 6.5 m.
4.9*t^2 = 6.5
t^2 = 1.327
Tf = 1.15 s. = Fall time.
d = Xo * Tf = 4.0m/s * 1.15s = 4.60 m.
To find the answer to question 1, we can use the formula:
Speed = Distance / Time
a) To calculate the total time of travel:
Distance 1 = 800 m
Speed 1 = 6.00 m/s
We can rearrange the formula to solve for time:
Time 1 = Distance 1 / Speed 1
Substituting the values:
Time 1 = 800 m / 6.00 m/s = 133.33 s (rounded to two decimal places)
Distance 2 = 800 m
Speed 2 = 8.00 m/s
Similarly, for the second distance:
Time 2 = Distance 2 / Speed 2
Time 2 = 800 m / 8.00 m/s = 100 s
Total Time = Time 1 + Time 2
Total Time = 133.33 s + 100 s = 233.33 s (rounded to two decimal places)
So the total time of travel is 233.33 seconds.
b) To calculate the average speed:
Average Speed = Total Distance / Total Time
Total Distance = Distance 1 + Distance 2 = 800 m + 800 m = 1600 m
Average Speed = 1600 m / 233.33 s = 6.86 m/s (rounded to two decimal places)
Therefore, the average speed is 6.86 m/s.
Moving on to question 2:
To find how far the can lands from the base of the rock, we can use the equations of motion for horizontal projectile motion.
The time it takes for the can to hit the ground can be found using the formula:
Time = sqrt(2h / g)
where h is the initial height (6.5 m) and g is the acceleration due to gravity (9.8 m/s^2).
Substituting the values:
Time = sqrt(2 * 6.5 m / 9.8 m/s^2) ≈ 0.907 s
The horizontal distance traveled by the can can be calculated using the formula:
Distance = Speed * Time
Speed = 4.0 m/s (given)
Substituting the values:
Distance = 4.0 m/s * 0.907 s ≈ 3.63 m
Therefore, the can will land approximately 3.63 meters from the base of the rock.