Explanation:

(b)

The horizontal component of velocity is constant so we can write:

d

=

v

x

t

d

=

v

cos

θ

t

d

=

40

×

cos

30

×

5

=

173

x

m

(a)

I'll set the point of launch to be the origin and use the convention that "up is +ve".

We can use:

s

=

u

t

+

1

2

a

t

2

This becomes:

h

=

v

y

t

−

1

2

g

t

2

h

=

v

sin

θ

t

−

1

2

g

t

2

h

=

40

sin

30

×

5

−

1

2

×

9.81

×

5

2

x

m

h

=

100

−

122.625

=

−

22.625

x

m

This means that the top of the tower is 23 m above the ground.