Answer:
(a). The distance is 49.79 m.
(b). The speed of the ball is 24.39 m/s.
Step-by-step explanation:
Given that,
Speed = 20 m/s
Angle = 40°
Height = 22 m
Time = 3.25 sec
(a). We need to calculate the distance
Using formula of distance
![d=u\cos\theta* t](https://img.qammunity.org/2020/formulas/physics/college/a9s72glxkhuku54yx6prxnx6xs506nuaz2.png)
Put the value into the formula
![d=20\cos40*3.25](https://img.qammunity.org/2020/formulas/physics/college/66ca00ky5jybazodee9x9r9ontxfmoousa.png)
![d=49.79\ m](https://img.qammunity.org/2020/formulas/physics/college/jpsjey6obi83jmq5jn2fkcjijnmv6fsabs.png)
(b). We need to calculate the horizontal velocity
Using formula of velocity
![v_(x)=u\cos\theta](https://img.qammunity.org/2020/formulas/physics/college/92t2d9ifm05sd37esc89ix20wna9ub761d.png)
Put the value into the formula
![v_(x)=20*\cos40](https://img.qammunity.org/2020/formulas/physics/college/83ajgn7e5fg3fa9172bmt64h7e70lvoin3.png)
![v_(x)=15.3\ m/s](https://img.qammunity.org/2020/formulas/physics/college/fyis87gspgduda1npbn5sr1ufgve6nr9az.png)
We need to calculate the vertical velocity
Using equation of motion
![v_(y)=u\sin\theta-gt](https://img.qammunity.org/2020/formulas/physics/college/ffv76uc521hc16gqpy7p54vw8qjev1f7b3.png)
Put the value into the formula
![v_(y)=20\sin40-9.8*3.25](https://img.qammunity.org/2020/formulas/physics/college/2pc03md02o1tdqkecazg96q99ox3d5o5ey.png)
![v_(y)=-19\ m/s](https://img.qammunity.org/2020/formulas/physics/college/cf525fu5j408842d9vqagtyqj8okg2dzkf.png)
Negative sign shows the opposite direction.
We need to calculate the speed of ball
Using formula of speed
![v=\sqrt{v_(x)^2+v_(y)^2}](https://img.qammunity.org/2020/formulas/physics/college/az2vzusqx8yquom1729qn6wgyax76km1ur.png)
![v=√((15.3)^2+(19)^2)](https://img.qammunity.org/2020/formulas/physics/college/nesbjl9rlu4n3bsoutgsx4s5ruoe9oj6h8.png)
![v=24.39\ m/s](https://img.qammunity.org/2020/formulas/physics/college/sc9s2282vnlsf3z9ww4ks23bo19lpkv2v4.png)
Hence, (a). The distance is 49.79 m.
(b). The speed of the ball is 24.39 m/s.