Aussie NSW Year 12 Projectile Motion Question.

[f3nr15]

Homework Statement

A projectile has a time of flight 7.5s and a range 1200m
calculate
(a) its horizontal velocity
(b) Its maximum height
(c) the velocity witch which it is produced

I take a_y as -9.8ms^-2

Homework Equations

r = u_xt
d_y = u_yt + (a_yt²/2)
v_y² = u_y² + 2ah
u_x² + u_y² = u
v = u + at

The Attempt at a Solution

I hope I am the correct

a) r = u_xt

u_x = r/t
u_x = 1200/7.5
u_x = 160m

.: Initial Horizontal Velocity is 160m

b)

d_y = u_yt + (at²/2)

d_y = 0 (Total vertical displacement is zero)
0 = 7.5u_y - 275.625
7.5u_y = 275.625
u_y = 36.75

v_y² = u_y² + 2ah

v_y = 0
0 = 1350.5625 - 19.6h
19.6h = 1350.5625
h = 68.90625 ...

.: Maximum height is 68.91m^-1

c)

u_x² + u_y² = u

(160)² + (36.75)² = 26950.5625
u = 164.1662648 ...

.: Initial Velocity is 164.17ms^-1

v = u + at

v = (164.1662648) + (-9.8)(7.5)
v = 90.6662648 ...

.: Final Velocity is 90.67ms^-1


Ya ?

 

[PhanthomJay]

Homework Statement

A projectile has a time of flight 7.5s and a range 1200m
calculate
(a) its horizontal velocity
(b) Its maximum height
(c) the velocity witch which it is produced

I take a_y as -9.8ms^-2

Homework Equations

r = u_xt
d_y = u_yt + (a_yt²/2)
v_y² = u_y² + 2ah
u_x² + u_y² = u
v = u + at

The Attempt at a Solution

I hope I am the correct

a) r = u_xt

u_x = r/t
u_x = 1200/7.5
u_x = 160m

.: Initial Horizontal Velocity is 160m

b)

d_y = u_yt + (at²/2)

d_y = 0 (Total vertical displacement is zero)
0 = 7.5u_y - 275.625
7.5u_y = 275.625
u_y = 36.75

v_y² = u_y² + 2ah

v_y = 0
0 = 1350.5625 - 19.6h
19.6h = 1350.5625
h = 68.90625 ...

.: Maximum height is 68.91m^-1

c)

u_x² + u_y² = u

(160)² + (36.75)² = 26950.5625
u = 164.1662648 ...

.: Initial Velocity is 164.17ms^-1

v = u + at

v = (164.1662648) + (-9.8)(7.5)
v = 90.6662648 ...

.: Final Velocity is 90.67ms^-1


Ya ?

a, b, and c look correct numerically, but your units generally are not. Then you added a part d which is not correct. You've got to look in the vertical and horizontal direction separately. Since energy is conserved, what might the final velocity be?

 

[m2003]

I would say that your calculations and equations appear to be correct. However, it would be helpful to show your units in your calculations, as it is important to keep track of the units in order to get the correct final answer. Also, it would be helpful to explain your reasoning behind using certain equations and how they relate to the given information. Overall, it seems like you have a good understanding of projectile motion and were able to successfully solve the problem.