50m M The diagram above shows a projectile launched from 50 metres above a fixed origin O. The initial velocity is V ms¯' at a fixed angle 0 above the horizontal . M is the point where the projectile meets the horizontal and P is the highest point of the flight above the horizontal. Z is the point of projection with OZ = 50 metres. During the time of motion: Horizontal displacement x = 30-/3t Vertical displacement y = -5t² +30t + 50 [all displacements are in metres and time, t , is in seconds with t2 0] (i) Find correct to one decimal the time taken to reach M. (ii) What is the distance from O to M? [Give your answer to the nearest whole metre] (iii) When will the projectile reach P? (iv) How high is P above the horizontal?
50m M The diagram above shows a projectile launched from 50 metres above a fixed origin O. The initial velocity is V ms¯' at a fixed angle 0 above the horizontal . M is the point where the projectile meets the horizontal and P is the highest point of the flight above the horizontal. Z is the point of projection with OZ = 50 metres. During the time of motion: Horizontal displacement x = 30-/3t Vertical displacement y = -5t² +30t + 50 [all displacements are in metres and time, t , is in seconds with t2 0] (i) Find correct to one decimal the time taken to reach M. (ii) What is the distance from O to M? [Give your answer to the nearest whole metre] (iii) When will the projectile reach P? (iv) How high is P above the horizontal?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![y
P
50m
X
M
The diagram above shows a projectile launched from 50 metres above a fixed
origin O. The initial velocity is V ms at a fixed angle 0 above the horizontal .
M is the point where the projectile meets the horizontal and P is the highest
point of the flight above the horizontal. Z is the point of projection with
OZ = 50 metres. During the time of motion:
Horizontal displacement x = 30/3t
Vertical displacement y = -5t² +30t + 50
[all displacements are in metres and time, t , is in seconds with t2 0]
(i) Find correct to one decimal the time taken to reach M.
(ii) What is the distance from O to M? [Give your answer to the nearest
whole metre]
(iii) When will the projectile reach P?
(iv) How high is P above the horizontal?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc39c8175-b821-4fba-9e67-9800dcabcff6%2Fbc602559-4254-4971-b10a-d5a75043292b%2Felarg8t_processed.png&w=3840&q=75)
Transcribed Image Text:y
P
50m
X
M
The diagram above shows a projectile launched from 50 metres above a fixed
origin O. The initial velocity is V ms at a fixed angle 0 above the horizontal .
M is the point where the projectile meets the horizontal and P is the highest
point of the flight above the horizontal. Z is the point of projection with
OZ = 50 metres. During the time of motion:
Horizontal displacement x = 30/3t
Vertical displacement y = -5t² +30t + 50
[all displacements are in metres and time, t , is in seconds with t2 0]
(i) Find correct to one decimal the time taken to reach M.
(ii) What is the distance from O to M? [Give your answer to the nearest
whole metre]
(iii) When will the projectile reach P?
(iv) How high is P above the horizontal?
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