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Initial Velocity and Launch Angle
Initial horizontal velocity: `u_x/u=costheta` Initial vertical velocity: `u_y/u=sintheta`
`(u_y)/(u_x)=tantheta`
`u^2=(u_x)^2+(u_y)^2` `u=sqrt((u_x)^2+(u_y)^2)` The initial velocity can be negative because the initial direction of a projectile can also be downwards as shown below. Situations in which this type of initial velocity occurs will be explored and clarified in practice questions later.
Practice Question 1A projectile is launched at 60 ms-1 at an elevation of 300. Find its initial horizontal and vertical velocities. Construct a right-angled triangle from vectors: Initial horizontal velocity: `u_x=60cos30^o` Initial vertical velocity: `u_y=60sin30^o`
Changes in Vertical Velocity
s represents the vertical displacement, ay represents the acceleration in the vertical axis (gravity), uy and vy are the initial vertical velocity and velocity after time t of the object during its projectile motion. Practice Question 2The initial vertical velocity of an object during projectile motion is 15 ms-1. The launch angle is `30^o`. (a) Calculate the initial horizontal velocity. (b) Calculate the vertical velocity and the instantaneous velocity 2 seconds after the object’s launch. The vertical velocity can be modelled by the following equation: `v_y=u_y+a_yt` Since, acceleration due to gravity is acting against the direction of the object, a negative sign must be placed in front of 9.8. The instantaneous velocity can be determined using Pythagoras’s theorem: `v=sqrt((25.98)^2+(-4.6)^2)` Since velocity is a vector quantity, a direction is needed. The direction is typically indicated by the angle relative to the horizontal. Using trigonometry: Therefore, the instantaneous velocity of the object 2 seconds after launch is 26.4 ms-1 10.0° relative to the horizontal axis.
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Answer: The horizontal velocity of a projectile is constant (a never changing in value), There is a vertical acceleration caused by gravity; its value is 9.8 m/s/s, down, The vertical velocity of a projectile changes by 9.8 m/s each second, The horizontal motion of a projectile is independent of its vertical motion. |