`\color{red} ✍️` An object that is in flight after being thrown or projected is called a `text(projectile)`. Such a projectile might be a football, a cricket ball, a baseball or any other object.
`\color{red} ✍️` The motion of a projectile may be thought of as the result of two separate, simultaneously occurring components of motions.
• In our discussion, we shall assume that the air resistance has negligible effect on the motion of the projectile.
Suppose that the projectile is launched with velocity `vecv_o` that makes an angle `theta_o` with the x-axis as shown in Fig.
After the object has been projected, the acceleration acting on it is that due to gravity which is directed vertically downward:
`veca=-ghatj`
Or, `a_x=0, a_y=-g`
`color(green)("The components of initial velocity")` `vecv_o` are:
`color(green)(v_(o x)=v_o cos theta_o)`
`color(green)(v_(o y)=v_o sin theta_o)`
If we take the initial position to be the origin of the reference frame as shown in Fig. We have,
`x_o=0, y_o=0`
Then, `x=x_0+v_(0x)t+1/2a_xt^2`
`x=v_(o x)t=(v_o cos theta_o)t`
and `y=y_0+v_(0y)t+1/2a_yt^2`
`y=(v_o sin theta_o)t-1/2 g t^2`
These equations give the x-, and y-coordinates of the position of a projectile at time t in terms of two parameters — initial speed `v_o` and projection angle `theta_o`.
• One of the components of velocity, i.e. x-component remains constant throughout the motion and only the y- component changes, like an object in free fall in vertical direction.
The components of velocity at time t can be obtained using `v_x = v_(o x) + a_xt` and `v_y= v_(oy) a_yt`.
so, `v_x=v_(o x)=v_ocos theta_o`
`v_y=v_o sin theta_o -g t`
• Note that at the point of maximum height, `v_y=0`, `:. theta=tan^(-1)((v_y)/(v_x))=0`
`\color{red} ✍️` An object that is in flight after being thrown or projected is called a `text(projectile)`. Such a projectile might be a football, a cricket ball, a baseball or any other object.
`\color{red} ✍️` The motion of a projectile may be thought of as the result of two separate, simultaneously occurring components of motions.
• In our discussion, we shall assume that the air resistance has negligible effect on the motion of the projectile.
Suppose that the projectile is launched with velocity `vecv_o` that makes an angle `theta_o` with the x-axis as shown in Fig.
After the object has been projected, the acceleration acting on it is that due to gravity which is directed vertically downward:
`veca=-ghatj`
Or, `a_x=0, a_y=-g`
`color(green)("The components of initial velocity")` `vecv_o` are:
`color(green)(v_(o x)=v_o cos theta_o)`
`color(green)(v_(o y)=v_o sin theta_o)`
If we take the initial position to be the origin of the reference frame as shown in Fig. We have,
`x_o=0, y_o=0`
Then, `x=x_0+v_(0x)t+1/2a_xt^2`
`x=v_(o x)t=(v_o cos theta_o)t`
and `y=y_0+v_(0y)t+1/2a_yt^2`
`y=(v_o sin theta_o)t-1/2 g t^2`
These equations give the x-, and y-coordinates of the position of a projectile at time t in terms of two parameters — initial speed `v_o` and projection angle `theta_o`.
• One of the components of velocity, i.e. x-component remains constant throughout the motion and only the y- component changes, like an object in free fall in vertical direction.
The components of velocity at time t can be obtained using `v_x = v_(o x) + a_xt` and `v_y= v_(oy) a_yt`.
so, `v_x=v_(o x)=v_ocos theta_o`
`v_y=v_o sin theta_o -g t`
• Note that at the point of maximum height, `v_y=0`, `:. theta=tan^(-1)((v_y)/(v_x))=0`