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?