. A body is thrown vertically upwards. If it travels
equal distances in 4th and 7th seconds of motion,
then the maximum height attained by the body is
(1) 125 m
(2) 100 m
(3) 50 m
(4) 75 m
Answers
Hi,
Answer: option(1): 125 m
Explanation:
It is given that a body is thrown vertically upwards.
Let the distance travelled by the body in 4th & 7th second of the motion be denoted as “S4” & “S7” respectively.
Step 1: calculating the value of S4
Here t = 4 seconds and g = 10 m/s²
∴ St = u – [(g/2)(2t – 1)]
⇒ S4 = u – [(10/2)(2×4 - 1)]
⇒ S4 = (u – 35) m…… (i)
Step 2: calculating the value of S7
Here t = 7 seconds and g = 10 m/s²
∴ S7 = u – [(10/2)(2×7 - 1)]
⇒ S7 = (u – 65) m…… (ii)
Step 3:
Given that the body travels equal distances in 4th and 7th seconds of motion i.e.,
S4 = - S7
Substituting the values from (i) & (ii), we get
⇒ u - 35 = - ( u - 65)
⇒ u - 35 = - u + 65
⇒ 2u = 100
⇒ u = 50 m/s …. (iii)
Step 4:
Thus,
The maximum height “H” attained by the body is,
= u² / 2g
= (50)² / (2*10) ….. [substituting value of u from (iii)]
= 2500 / 20
= 125 m
Hope this is helpful!!!!