Projectile Motion Question Help (1 Viewer)

[itsalberttrinh]

A missile is fired with speed Vm/s at an angle of elevation 'α'. After 21 seconds it hits a target with a horizontal distance of 1680m and a vertical distance of 945m. Take g = 10m/s/s

i) Find speed and angle of projection (nearest degree)

No Answers soz
Thanks

 

[Carrotsticks]

x=Vtcos(a), sub x=1680, t=21 to get some expression with V and cos(a).

y=-5t^2 + Vtsin(a), sub y=945, t=21 to get another expression with V and sin(a).

Two options from here, depending on whether you want to find V or (a) first.

To find (a) first, make V the subject of the first expression, then substitute into the second, then solve for (a). Or you can make sin(a) and cos(a) the subject of the second and first expressions respectively, then divide the two equations to get tan(a)=..., then solve for (a).

To find V first make cos(a) the subject of the first expression and sin(a) the subject of the second expression. Then use the fact that cos^2(a)+sin^2(a)=1 to eliminate the (a), leaving an expression with V, then solve for V.

EDIT: For these questions, I usually find (a) first (easier to find first than V), then substitute in to x=Vtcos(a) to find V.