A body is projected vertically upwards with a speed of 40 m/s.Find the distance travelled by body in last second of upward journey?(g=9.8m/s2 neglect effect of air resistance)
V = Vo + g*Tr = 0 at max. ht.
Tr = -Vo/g = -40/-9.8 = 4.08 s. = Rise
time.
T = 4.08-1 = 3.08 s.
h1 = Vo*t + 0.5g*t^2
h1 = 40*3.08 - 4.9*3.08^2 = 76.7 m.
h2 = 40*4.08 - 4.9*4.08^2 = 81.6 m.
h2-h1 = 81.6-76.7 = 4.93 m. = Distance traveled in the last second.
To find the distance traveled by the body in the last second of its upward journey, we need to determine the time it takes for the body to reach its maximum height.
Given:
Initial velocity, u = 40 m/s (upwards)
Acceleration due to gravity, g = 9.8 m/s^2
First, we can calculate the time it takes for the body to reach its maximum height using the following formula:
v = u - gt
where:
v = final velocity (when the body reaches its maximum height)
u = initial velocity
g = acceleration due to gravity
t = time
In this case, since the body is moving vertically upwards, its final velocity will be zero.
0 = 40 - 9.8t
Simplifying the equation:
9.8t = 40
t = 40 / 9.8
t ≈ 4.08 seconds (rounded to two decimal places)
Now, to find the distance traveled in the last second of the upward journey, we can subtract the distance covered in the first three seconds from the total distance covered in four seconds.
The distance traveled in the initial three seconds can be calculated using the formula:
s = ut + (1/2)gt^2
s = 40(3) + (0.5)(9.8)(3)^2
s = 120 + 44.1
s ≈ 164.1 meters (rounded to one decimal place)
The total distance traveled in four seconds is given by:
s_total = ut_total + (1/2)g(t_total)^2
s_total = 40(4) + (0.5)(9.8)(4)^2
s_total = 160 + 78.4
s_total ≈ 238.4 meters (rounded to one decimal place)
Finally, we can find the distance traveled in the last second by subtracting the distance traveled in the first three seconds from the total distance traveled in four seconds:
Distance traveled in the last second = s_total - s
Distance traveled in the last second ≈ 238.4 - 164.1
Distance traveled in the last second ≈ 74.3 meters (rounded to one decimal place)
Therefore, the body traveled approximately 74.3 meters in the last second of its upward journey.
To find the distance traveled by the body in the last second of the upward journey, we need to calculate the time it takes for the body to reach its highest point.
The formula for the time taken to reach the maximum height can be derived from the equation of motion:
v = u + gt
Where:
v = final velocity (0 m/s at the highest point)
u = initial velocity (40 m/s)
g = acceleration due to gravity (9.8 m/s^2)
t = time taken to reach the maximum height
Rearranging the equation, we have:
t = (v - u) / g
Substituting the given values:
t = (0 - 40) / (-9.8)
t = 4.08 seconds (approximately)
Now that we have the time taken to reach the maximum height, we can calculate the distance traveled during this time using the formula:
s = ut + (1/2) gt^2
Substituting the values:
s = (40 * 4.08) + (1/2) * (-9.8) * (4.08^2)
s = 163.2 - 82.65
s = 80.55 meters
Therefore, the distance traveled by the body in the last second of the upward journey is approximately 80.55 meters.